A025424 Number of partitions of n into 9 squares.

1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 3, 3, 4, 4, 4, 4, 5, 6, 6, 5, 7, 7, 7, 7, 8, 9, 9, 9, 9, 11, 11, 10, 12, 13, 12, 12, 15, 14, 16, 15, 15, 18, 17, 16, 18, 20, 19, 20, 20, 21, 23, 21, 23, 26, 28, 25, 27, 29, 28, 28, 28, 30, 33, 33, 30, 36, 35, 33, 38, 37, 40, 40, 41, 40, 44, 42, 41, 47, 48, 47, 48

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Programs

Maple

b:= proc(n, i, t) option remember; `if`(n=0, 1,
      `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), 9):
seq(a(n), n=0..120);  # Alois P. Heinz, May 30 2014

Mathematica

b[n_, i_, t_] := b[n, i, t] = If[n == 0, 1, 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, 9]; Table[a[n], {n, 0, 120}] (* Jean-François Alcover, Jun 11 2015, after Alois P. Heinz *)