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A025443 Number of partitions of n into 4 distinct nonzero squares. 23
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, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 3, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 2, 1, 0, 1, 2, 2, 0, 0, 1, 2, 0, 0, 3, 0, 0, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,79

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..20000

Index entries for sequences related to sums of squares

FORMULA

a(n) = [x^n y^4] Product_{k>=1} (1 + y*x^(k^2)). - Ilya Gutkovskiy, Apr 22 2019

MAPLE

b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=0, 1, 0),

      `if`(t*i^2<n, 0, `if`(i=1, 0, b(n, i-1, t))+

      `if`(i^2>n, 0, b(n-i^2, i-1, t-1))))

    end:

a:= n-> b(n, isqrt(n), 4):

seq(a(n), n=0..150);  # Alois P. Heinz, Feb 07 2013

MATHEMATICA

b[n_, i_, t_] := b[n, i, t] = If[n==0, If[t==0, 1, 0], If[t*i^2<n, 0, If[i == 1, 0, b[n, i-1, t]] + If[i^2>n, 0, b[n-i^2, i-1, t-1]]]]; a[n_] := b[n, Sqrt[n] // Floor, 4]; Table[a[n], {n, 0, 150}] (* Jean-Fran├žois Alcover, Feb 29 2016, after Alois P. Heinz*)

CROSSREFS

Cf. A025428 (not necessarily distinct), A025376-A025394 (subsequences), A025417 (greedy inverse).

Sequence in context: A265314 A307791 A307766 * A120080 A227570 A111700

Adjacent sequences:  A025440 A025441 A025442 * A025444 A025445 A025446

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified November 19 22:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)