OFFSET
0,4
COMMENTS
Also the number of nonnegative integer solutions (a_1, a_2, ... , a_n) to the equation a_1^2 + 2*a_2^2 + ... + n*a_n^2 = n^3.
EXAMPLE
1*0^2 + 2*0^2 + 3*0^2 + 4*4^2 = 64.
1*0^2 + 2*0^2 + 3*4^2 + 4*2^2 = 64.
1*1^2 + 2*0^2 + 3*3^2 + 4*3^2 = 64.
1*1^2 + 2*4^2 + 3*3^2 + 4*1^2 = 64.
1*2^2 + 2*2^2 + 3*4^2 + 4*1^2 = 64.
1*2^2 + 2*4^2 + 3*2^2 + 4*2^2 = 64.
1*4^2 + 2*0^2 + 3*2^2 + 4*3^2 = 64.
1*4^2 + 2*0^2 + 3*4^2 + 4*0^2 = 64.
1*4^2 + 2*4^2 + 3*0^2 + 4*2^2 = 64.
1*4^2 + 2*4^2 + 3*2^2 + 4*1^2 = 64.
1*5^2 + 2*0^2 + 3*1^2 + 4*3^2 = 64.
1*5^2 + 2*2^2 + 3*3^2 + 4*1^2 = 64.
1*5^2 + 2*4^2 + 3*1^2 + 4*1^2 = 64.
1*6^2 + 2*0^2 + 3*2^2 + 4*2^2 = 64.
1*7^2 + 2*2^2 + 3*1^2 + 4*1^2 = 64.
1*8^2 + 2*0^2 + 3*0^2 + 4*0^2 = 64.
So a(4) = 16.
PROG
(PARI) {a(n) = polcoeff(prod(i=1, n, sum(j=0, sqrtint(n^3\i), x^(i*j^2)+x*O(x^(n^3)))), n^3)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 01 2018
STATUS
approved