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A025431 Number of partitions of n into 7 nonzero squares. 18
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, 3, 1, 2, 3, 1, 1, 4, 2, 3, 4, 1, 4, 3, 1, 5, 4, 3, 4, 4, 4, 3, 4, 4, 5, 7, 3, 5, 7, 3, 5, 8, 4, 7, 7, 4, 8, 6, 3, 9, 10, 6, 8, 8, 7, 7, 8, 8, 9, 11, 7, 9, 12, 6, 8, 15, 8, 12, 12, 7, 15, 10, 8, 16, 13, 11, 13, 13, 12, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,23

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^7] Product_{k>=1} 1/(1 - y*x^(k^2)). - Ilya Gutkovskiy, Apr 19 2019

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

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, 7];

Table[a[n], {n, 0, 120}] (* Jean-Fran├žois Alcover, Apr 30 2018, after Alois P. Heinz *)

CROSSREFS

Column k=7 of A243148.

Sequence in context: A340101 A049847 A255274 * A161070 A161109 A161044

Adjacent sequences:  A025428 A025429 A025430 * A025432 A025433 A025434

KEYWORD

nonn,look

AUTHOR

David W. Wilson

STATUS

approved

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Last modified August 8 09:40 EDT 2022. Contains 356009 sequences. (Running on oeis4.)