A025433 Number of partitions of n into 9 nonzero squares.

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, 4, 2, 4, 4, 2, 4, 4, 2, 5, 6, 3, 5, 5, 4, 5, 5, 5, 6, 9, 5, 6, 9, 4, 7, 10, 5, 10, 9, 6, 11, 9, 6, 11, 13, 9, 11, 12, 9, 11, 13, 11, 14, 16, 11, 14, 16, 10, 13, 20, 13, 18, 19, 12, 20, 18, 13

Offset

0,25

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^9] Product_{k>=1} 1/(1 - y*x^(k^2)). - Ilya Gutkovskiy, Apr 19 2019

a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/6)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} A010052(i) * A010052(j) * A010052(k) * A010052(l) * A010052(m) * A010052(o) * A010052(p) * A010052(q) * A010052(n-i-j-k-l-m-o-p-q). - 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), 9):
seq(a(n), n=0..120);  # Alois P. Heinz, May 30 2014

Mathematica

a[n_] := Count[ PowersRepresentations[n, 9, 2], pr_List /; FreeQ[pr, 0]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Dec 27 2012 *)

Crossrefs

Column k=9 of A243148.

Sequence in context: A029325 A276417 A025432 * A025434 A111178 A279187

Adjacent sequences: A025430 A025431 A025432 * A025434 A025435 A025436

Keyword

nonn

Author

David W. Wilson

Status

approved