A025442 Number of partitions of n into 3 distinct nonzero squares.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 1, 1, 0, 0, 2, 1, 0, 0, 0, 2, 1, 0, 2, 1, 0, 0, 1, 0, 1, 1, 0, 2, 0, 0, 2, 2, 1, 0, 1, 2, 0, 0, 0, 2, 0, 0, 3, 0, 0, 1, 2, 1, 1

Offset

0,63

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)>0 <=> n is in A004432. - M. F. Hasler, Feb 03 2013

a(n) = [x^n y^3] 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`(i<1 or t<1, 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), 3):
seq(a(n), n=0..120);  # Alois P. Heinz, Feb 07 2013

Mathematica

b[n_, i_, t_] := b[n, i, t] = If[n==0, If[t==0, 1, 0], If[i<1 || t<1, 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, 3]; Table[a[n], {n, 0, 120}] (* Jean-François Alcover, Oct 10 2015, after Alois P. Heinz *)

Prog

(PARI) A025442(n)={sum(x=1, sqrtint(n\3), sum(y=x+1, sqrtint((n-1-x^2)\2), issquare(n-x^2-y^2)))} \\ - M. F. Hasler, Feb 03 2013

Crossrefs

Cf. A024803, A025339, A001974, A004432.

Column k=3 of A341040.

Sequence in context: A159708 A144625 A224772 * A260118 A128582 A213185

Adjacent sequences: A025439 A025440 A025441 * A025443 A025444 A025445

Keyword

nonn

Author

David W. Wilson

Status

approved