OFFSET
0,24
LINKS
FORMULA
a(n) = [x^n y^8] Product_{k>=1} 1/(1 - y*x^(k^2)). - Ilya Gutkovskiy, Apr 19 2019
a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} A010052(i) * A010052(j) * A010052(k) * A010052(l) * A010052(m) * A010052(o) * A010052(p) * A010052(n-i-j-k-l-m-o-p). - Wesley Ivan Hurt, Apr 19 2019
MAPLE
b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
`if`(i<1 or t<1, 0, b(n, i-1, t)+
`if`(i^2>n, 0, b(n-i^2, i, t-1))))
end:
a:= n-> b(n, isqrt(n), 8):
seq(a(n), n=0..120); # Alois P. Heinz, May 30 2014
MATHEMATICA
b[n_, i_, t_] := b[n, i, t] = If[n == 0, If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] + If[i^2 > n, 0, b[n - i^2, i, t - 1]]]];
a[n_] := b[n, Sqrt[n] // Floor, 8];
Table[a[n], {n, 0, 120}] (* Jean-François Alcover, May 20 2018, after Alois P. Heinz *)
Table[Count[IntegerPartitions[n, {8}], _?(AllTrue[Sqrt[#], IntegerQ]&)], {n, 0, 100}] (* Harvey P. Dale, Jul 20 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved