A331844 Number of compositions (ordered partitions) of n into distinct squares.

1, 1, 0, 0, 1, 2, 0, 0, 0, 1, 2, 0, 0, 2, 6, 0, 1, 2, 0, 0, 2, 6, 0, 0, 0, 3, 8, 0, 0, 8, 30, 0, 0, 0, 2, 6, 1, 2, 6, 24, 2, 8, 6, 0, 0, 8, 30, 0, 0, 7, 32, 24, 2, 8, 30, 120, 6, 24, 2, 6, 0, 8, 36, 24, 1, 34, 150, 0, 2, 12, 30, 24, 0, 2, 38, 150, 0, 12, 78, 144, 2

Offset

0,6

Links

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

Index entries for sequences related to compositions

Index entries for sequences related to sums of squares

Example

a(14) = 6 because we have [9,4,1], [9,1,4], [4,9,1], [4,1,9], [1,9,4] and [1,4,9].

Maple

b:= proc(n, i, p) option remember;
      `if`(i*(i+1)*(2*i+1)/6<n, 0, `if`(n=0, p!,
      `if`(i^2>n, 0, b(n-i^2, i-1, p+1))+b(n, i-1, p)))
    end:
a:= n-> b(n, isqrt(n), 0):
seq(a(n), n=0..82);  # Alois P. Heinz, Jan 30 2020

Mathematica

b[n_, i_, p_] := b[n, i, p] = If[i(i+1)(2i+1)/6 < n, 0, If[n == 0, p!, If[i^2 > n, 0, b[n - i^2, i - 1, p + 1]] + b[n, i - 1, p]]];
a[n_] := b[n, Sqrt[n] // Floor, 0];
a /@ Range[0, 82] (* Jean-François Alcover, Oct 29 2020, after Alois P. Heinz *)

Crossrefs

Cf. A000290, A006456, A032020, A032021, A032022, A033461, A218396, A219107, A331843, A331845, A331846, A331847.

Sequence in context: A120630 A248509 A281542 * A191410 A249142 A225099

Adjacent sequences: A331841 A331842 A331843 * A331845 A331846 A331847

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 29 2020

Status

approved