Little math problems July 2019

[Albert Chan]

Hi, Jim Horn

Thanks !

Consider only 1 of the 4 rectangle, size n x (n+1), total 1-way distance traveled f(n)

XCas> f(n) := sum(sum(a+b, a = 1 .. n), b = 0 .. n) // → n*(n+1)*(2n+1)/2
XCas> n := (x-1)/2         // since x = n + (n+1)
XCas> expand( 8*f(n) )   // → x³ - x

Trivia, f(n) happened to be 3 * sum(k^2, k=1 .. n)