Difference of the square of the sum

Question

Find the difference between the square of the sums and sum of the squares.

This is the mathematical representation:

\$\left(\sum n\right)^2-\sum n^2\$

Your program/method should take two inputs, these are your lower and upper limits of the range, and are inclusive. Limits will be whole integers above 0.

Your program/method should return the answer.

You may use whichever base you would like to, but please state in your answer which base you have used.

Test case (Base 10)

5,9      970
91,123   12087152
1,10     2640

This is usual code-golf, so the shorter the answer the better.

Answer 1

Perl 5.10, 41 bytes

map{$s+=$_,$r+=$_**2}(<>..<>);say$s**2-$r

Input is given on 2 lines, for instance:

61
127

Try it here!

Answer 2

CoffeeScript, 49 Bytes

f=(n,m,s=0)->if n>m then 0else 2*n*s+f(n+1,m,n+s)

Translation of Neil's answer

Output:

f 91, 123 == 12087152 => true

Answer 3

Python 2.7, 82 bytes 85 bytes

def a(l, u):
    c=0
    d=0
    for e in range(l, u+1):
        c+=e
        d+=e**2
    return c**2-d

Works in base 10.

Answer 4

Julia 0.6, 21 bytes

r->2triu(r*r',1)|>sum

Try it online!

Julia port of Luis Mendo's MATL answer. Comes out to the same bytecount as the other Julia answer by @gggg. Takes a Range similar to that answer, does a matrix multiply of it with its transpose to get all pairwise products in a matrix. Takes the upper triangular portion of that (the 1 argument is to denote the distance from the leading diagonal to start from), multiplies that by 2, and finally sums the values and returns that implicitly.

Answer 5

Wolfram Language (Mathematica), 18 bytes

Tr@#^2-#.#&@*Range

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Composition of Tr@#^2-#.#& (square of sum minus sum of squares, where sum of squares is implemented via dot product) and Range (list of all integers between the two inputs). If you like seeing the operations in order, Range/*Tr@#^2-#.#& is equivalent.

As a bonus, also solves this challenge with no modifications, since Range can either take one argument (giving the range from 1 to the input) or two. (But it's not the most efficient solution possible there.)

Answer 6

Bash, 74 65 bytes

x=y=0;for i in `seq $1 $2`;{ x=$[x+i];y=$[y+i*i]; };echo $[x*x-y]

Try it online!

I'm no expert at bash golfing, but this works.
Managed to cut 9 bytes just by reading through the bash golfing tips thread

Answer 7

Tcl, 105 bytes

proc d a\ b {while {[incr a]<=$b} {set j $a
while \$j<=$b {incr p [expr 2*([incr j]-1)*($a-1)]}}
expr $p}

Try it online!

# Tcl, 112 bytes

proc d a\ b {set i [expr $a-1]
while \$i<$b {set j [incr i]
while \$j<$b {incr p [expr 2*[incr j]*$i]}}
expr $p}

Answer 8

Factor + math.unicode, 34 bytes

[ [a,b] dup Σ sq swap norm-sq - ]

Try it online!

• [a,b] Create a range from the input.
• dup Σ sq swap Square of sum.
• norm-sq Sum of squares.
• - Subtract.