Сума квадратів перших десяти натуральних чисел дорівнює, $1^2 + 2^2 + \dots + 10^2 = 385$

Квадрат суми перших десяти натуральних чисел дорівнює,

$(1 + 2 + ... + 10)^2 = 55^2 = 3025$

Звідси різниця між сумою квадратів перших десяти натуральних чисел і квадратом суми

$3025 − 385 = 2640$

Для заданого вводу n знайдіть різницю між сумою квадратів перших n натуральних чисел та квадратом суми.

Тестові справи

1       => 0
2       => 4
3       => 22
10      => 2640
24      => 85100
100     => 25164150

Цей виклик вперше було оголошено на проекті Euler №6 .

Критерії виграшу

• Не існує правил щодо того, якою має бути поведінка з негативним або нульовим введенням.

• Найкоротша відповідь виграє.

Желе ,  5  4 байти

Ḋ²ḋṖ

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Як?

Реалізує $\sum_{i=2}^n{(i^2(i-1))}$ ...

Ḋ²ḋṖ - Link: non-negative integer, n
Ḋ    - dequeue (implicit range)       [2,3,4,5,...,n]
 ²   - square (vectorises)            [4,9,16,25,...,n*n]
   Ṗ - pop (implicit range)           [1,2,3,4,...,n-1]
  ḋ  - dot product                    4*1+9*2+16*3+25*4+...+n*n*(n-1)

Python 3 ,  28  27 байт

-1 завдяки xnor

lambda n:(n**3-n)*(n/4+1/6)

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Реалізатори $n(n-1)(n+1)(3n+2)/12$

Python 2,  29  28 байт:lambda n:(n**3-n)*(3*n+2)/12

APL (Dyalog Unicode) , 10 байт

1⊥⍳×⍳×1-⍨⍳

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Як це працює

1⊥⍳×⍳×1-⍨⍳
  ⍳×⍳×1-⍨⍳  Compute (x^3 - x^2) for 1..n
1⊥          Sum

Використовує той факт, що "квадрат суми" дорівнює "сумі кубів".

TI-Basic (серія TI-83), 12 11 байт

sum(Ans² nCr 2/{2,3Ans

Реалізація $\binom{n^2}{2}(\frac12 + \frac1{3n})$. Бере введення вAns: наприклад, запустіть10:prgmXдля обчислення результату для введення10.

Мозг-Флак , 74 72 68 64 байт

((([{}])){({}())}{})([{({}())({})}{}]{(({}())){({})({}())}{}}{})

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Досить простий спосіб зробити це за допомогою декількох складних змін. Сподіваємось, хтось знайде ще кілька хитрощів, щоб зробити це ще коротше.

Вугілля деревне , 12 10 байт

ＩΣＥＮ×ιＸ⊕ι²

$( \sum_1^n x )^2 = \sum_1^n x^3$$( \sum_1^n x )^2 - \sum_1^n x^2 = \sum_1^n (x^3 - x^2) = \sum_1^n (x - 1)x^2 = \sum_0^{n-1} x(x + 1)^2$

   Ｎ        Input number
  Ｅ         Map over implicit range i.e. 0 .. n - 1
        ι   Current value
       ⊕    Incremented
         ²  Literal 2
      Ｘ     Power
     ι      Current value
    ×       Multiply
 Σ          Sum
Ｉ           Cast to string
            Implicitly print

Perl 6 , 22 байти

{sum (1..$_)>>²Z*^$_}

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$\sum_{i=1}^n {(i^2(i-1))}$

Japt -x, 9 8 5 4 bytes

õ²í*

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Explanation

õ        :Range [1,input]
 ²       :Square each
  í      :Interleave with 0-based indices
   *     :Reduce each pair by multiplication
         :Implicit output of the sum of the resulting array

JavaScript, 20 bytes

f=n=>n&&n*n*--n+f(n)

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APL(Dyalog), 17 bytes

{+/(¯1↓⍵)×1↓×⍨⍵}⍳

(Much longer) Port of Jonathan Allan's Jelly answer.

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APL (Dyalog), 16 bytes

((×⍨+/)-(+/×⍨))⍳

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 (×⍨+/)            The square (× self) of the sum (+ fold)
       -           minus
        (+/×⍨)     the sum of the square
(             )⍳   of [1, 2, … input].

Mathematica, 21 17 bytes

^{-4 bytes thanks to alephalpha.}

(3#+2)(#^3-#)/12&

Pure function. Takes an integer as input and returns an integer as output. Just implements the polynomial, since Sums, Ranges, Trs, etc. take up a lot of bytes.

Java (JDK), 23 bytes

n->(3*n+2)*(n*n*n-n)/12

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dc, 16 bytes

?dd3^r-r3*2+*C/p

Implements $(n^3-n)(3n+2)/12$

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05AB1E, 8 bytes

ÝDOnsnO-

Explanation:

ÝDOnsnO-     //Full program
Ý            //Push [0..a] where a is implicit input
 D           //Duplicate top of stack
  On         //Push sum, then square it
    s        //Swap top two elements of stack
     nO      //Square each element, then push sum
       -     //Difference (implicitly printed)

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C, C++, 46 40 37 bytes ( #define ), 50 47 46 bytes ( function )

-1 byte thanks to Zacharý

-11 bytes thanks to ceilingcat

Macro version :

#define F(n)n*n*~n*~n/4+n*~n*(n-~n)/6

Function version :

int f(int n){return~n*n*n*~n/4+n*~n*(n-~n)/6;}

Thoses lines are based on thoses 2 formulas :

Sum of numbers between 1 and n = n*(n+1)/2
Sum of squares between 1 and n = n*(n+1)*(2n+1)/6

So the formula to get the answer is simply (n*(n+1)/2) * (n*(n+1)/2) - n*(n+1)*(2n+1)/6

And now to "optimize" the byte count, we break parenthesis and move stuff around, while testing it always gives the same result

(n*(n+1)/2) * (n*(n+1)/2) - n*(n+1)*(2n+1)/6 => n*(n+1)/2*n*(n+1)/2 - n*(n+1)*(2n+1)/6 => n*(n+1)*n*(n+1)/4 - n*(n+1)*(2n+1)/6

Notice the pattern p = n*n+1 = n*n+n, so in the function, we declare another variable int p = n*n+n and it gives :

p*p/4 - p*(2n+1)/6

For p*(p/4-(2*n+1)/6) and so n*(n+1)*(n*(n+1)/4 - (2n+1)/6), it works half the time only, and I suspect integer division to be the cause ( f(3) giving 24 instead of 22, f(24) giving 85200 instead of 85100, so we can't factorize the macro's formula that way, even if mathematically it is the same.

Both the macro and function version are here because of macro substitution :

F(3) gives 3*3*(3+1)*(3+1)/4-3*(3+1)*(2*3+1)/6 = 22
F(5-2) gives 5-2*5-2*(5-2+1)*(5-2+1)/4-5-2*(5-2+1)*(2*5-2+1)/6 = -30

and mess up with the operator precedence. the function version does not have this problem

JavaScript (ES6), 22 bytes

n=>n*~-n*-~n*(n/4+1/6)

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Pyth, 7 bytes

sm**hdh

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Uses the formula in Neil's answer.

sm**hdhddQ   Implicit: Q=eval(input())
             Trailing ddQ inferred
 m       Q   Map [0-Q) as d, using:
    hd         Increment d
   *  hd       Multiply the above with another copy
  *     d      Multiply the above by d
s            Sum, implicit print 

SNOBOL4 (CSNOBOL4), 70 69 bytes

 N =INPUT
I X =X + N ^ 3 - N ^ 2
 N =GT(N) N - 1 :S(I)
 OUTPUT =X
END

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Pari/GP, 21 bytes

n->(3*n+2)*(n^3-n)/12

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05AB1E, 6 bytes

LnDƶαO

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Explanation

L         # push range [1 ... input]
 n        # square each
  D       # duplicate
   ƶ      # lift, multiply each by its 1-based index
    α     # element-wise absolute difference
     O    # sum

Some other versions at the same byte count:

L<ān*O
Ln.āPO
L¦nā*O

R, 28 bytes

x=1:scan();sum(x)^2-sum(x^2)

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MathGolf, 6 bytes

{î²ï*+

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Calculates $\sum_{k=1}^n (k^2(k-1))$

Explanation:

{       Loop (implicit) input times
 î²     1-index of loop squared
    *   Multiplied by
   ï    The 0-index of the loop
     +  And add to the running total

Clojure, 58 bytes

(fn[s](-(Math/pow(reduce + s)2)(reduce +(map #(* % %)s))))

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Edit: I misunderstood the question

Clojure, 55, 35 bytes

#(* %(+ 1 %)(- % 1)(+(* 3 %)2)1/12)

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cQuents, 17 15 bytes

b$)^2-c$
;$
;$$

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Explanation

 b$)^2-c$     First line
:             Implicit (output nth term in sequence)
 b$)          Each term in the sequence equals the second line at the current index
    ^2        squared
      -c$     minus the third line at the current index

;$            Second line - sum of integers up to n
;$$           Third line - sum of squares up to n

APL(NARS), 13 chars, 26 bytes

{+/⍵×⍵×⍵-1}∘⍳

use the formula Sum'w=1..n'(ww(w-1)) possible i wrote the same some other wrote + or - as "1⊥⍳×⍳×⍳-1"; test:

  g←{+/⍵×⍵×⍵-1}∘⍳
  g 0
0
  g 1
0
  g 2
4
  g 3
22
  g 10
2640

Stax, 4 bytes

╡⌠(♠

Run and debug it

For all positive k integers up to the input, add k^2 * (k-1).

QBASIC, 45 44 bytes

Going pure-math saves 1 byte!

INPUT n
?n^2*(n+1)*(n+1)/4-n*(n+1)*(2*n+1)/6

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Previous, loop-based answer

INPUT n
FOR q=1TO n
a=a+q^2
b=b+q
NEXT
?b^2-a

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Note that the REPL is a bit more expanded because the interpreter fails otherwise.

JAEL, 13 10 bytes

#&àĝ&oȦ

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Explanation (generated automatically):

./jael --explain '#&àĝ&oȦ'
ORIGINAL CODE:  #&àĝ&oȦ

EXPANDING EXPLANATION:
à => `a
ĝ => ^g
Ȧ => .a!

EXPANDED CODE:  #&`a^g&o.a!

COMPLETED CODE: #&`a^g&o.a!,

#          ,            repeat (p1) times:
 &                              push number of iterations of this loop
  `                             push 1
   a                            push p1 + p2
    ^                           push 2
     g                          push p2 ^ p1
      &                         push number of iterations of this loop
       o                        push p1 * p2
        .                       push the value under the tape head
         a                      push p1 + p2
          !                     write p1 to the tapehead
            ␄           print machine state

05AB1E, 6 bytes

LDOšnÆ

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Explanation:

           # implicit input (example: 3)
L          # range ([1, 2, 3])
 DOš       # prepend the sum ([6, 1, 2, 3])
    n      # square each ([36, 1, 4, 9])
     Æ     # reduce by subtraction (22)
           # implicit output

Æ isn't useful often, but this is its time to shine. This beats the naïve LOnILnO- by two whole bytes.