A025434 - OEIS

A025434

Number of partitions of n into 10 nonzero squares.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 4, 1, 2, 4, 1, 2, 5, 2, 4, 4, 2, 5, 4, 2, 5, 6, 4, 5, 6, 4, 5, 6, 5, 7, 9, 5, 7, 10, 5, 7, 11, 6, 11, 10, 6, 12, 10, 7, 13, 14, 10, 12, 14, 11, 12, 14, 12, 16, 19, 12, 16, 19, 12, 16, 22, 15, 21, 21, 15

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OFFSET

0,26

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Index entries for sequences related to sums of squares

FORMULA

a(n) = [x^n y^10] Product_{k>=1} 1/(1 - y*x^(k^2)). - Ilya Gutkovskiy, Apr 19 2019

a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} A010052(i) * A010052(j) * A010052(k) * A010052(l) * A010052(m) * A010052(o) * A010052(p) * A010052(q) *A010052(r) * A010052(n-i-j-k-l-m-o-p-q-r). - 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), 10):

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, 10];

a /@ Range[0, 120] (* Jean-François Alcover, Nov 07 2020, after Alois P. Heinz *)

CROSSREFS