A025444 - OEIS

A025444

Number of partitions of n into 5 distinct nonzero squares.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 1, 0

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OFFSET

0,104

LINKS

David A. Corneth, Table of n, a(n) for n = 0..9999

Index entries for sequences related to sums of squares

FORMULA

a(n) = [x^n y^5] Product_{k>=1} (1 + y*x^(k^2)). - Ilya Gutkovskiy, Apr 22 2019

EXAMPLE

a(111) = 2 via 1 + 4 + 9 + 16 + 81 = 1 + 9 + 16 + 36 + 49. - David A. Corneth, Feb 02 2021

MAPLE

From R. J. Mathar, Oct 18 2010: (Start)

A025444aux := proc(n, m, nmax) local a, m, upn, lv ; if m = 1 then if issqr(n) and nmax^2 >= n and n >= 1 then return 1; else return 0; end if; else a := 0 ; for upn from 1 to nmax do lv := n-upn^2 ; if lv <0 then break; end if; a := a + procname(lv, m-1, upn-1) ; end do: return a; end if; end proc:

A025444 := proc(n) A025444aux(n, 5, n) ; end proc: (End)

CROSSREFS

Cf. A000290, A008452, A010052, A025433, A025441, A025442, A025443, A025444, A045851, A340946, A340988, A340998, A340999, A341000, A341001.

Column k=5 of A341040.

Sequence in context: A086260 A124505 A326855 * A212619 A309162 A345197

Adjacent sequences: A025441 A025442 A025443 * A025445 A025446 A025447

KEYWORD

nonn,look

AUTHOR

David W. Wilson

STATUS

approved