A025430 Number of partitions of n into 6 nonzero squares.

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, 1, 1, 2, 3, 1, 1, 3, 1, 1, 4, 1, 3, 3, 1, 4, 2, 1, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 6, 3, 4, 6, 2, 3, 7, 3, 6, 5, 2, 7, 5, 3, 7, 7, 5, 6, 6, 5, 5, 6, 6, 7, 9, 5, 6, 10, 4, 6, 11, 5, 10, 8, 6, 11, 7, 5, 11, 10, 8, 10, 8, 8, 8, 9, 10, 11, 13

Offset

0,22

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^6] Product_{k>=1} 1/(1 - y*x^(k^2)). - Ilya Gutkovskiy, Apr 19 2019

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

Mathematica

a[n_] := Count[PowersRepresentations[n, 6, 2], r_ /; FreeQ[r, 0]]; Array[a, 120, 0] (* Jean-François Alcover, Feb 19 2016 *)
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, 6];
a /@ Range[0, 120] (* Jean-François Alcover, Nov 06 2020, after Alois P. Heinz *)

Crossrefs

Column k=6 of A243148.

Sequence in context: A354579 A306261 A329722 * A256972 A365708 A352999

Adjacent sequences: A025427 A025428 A025429 * A025431 A025432 A025433

Keyword

nonn,easy

Author

David W. Wilson

Status

approved