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

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

Column k=10 of A243148.

Cf. A010052.

Sequence in context: A276417 A025432 A025433 * A111178 A279187 A254434

Adjacent sequences: A025431 A025432 A025433 * A025435 A025436 A025437

Keyword

nonn

Author

David W. Wilson

Status

approved