A331983 Number of compositions (ordered partitions) of n into distinct squares > 1.

1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 8, 0, 0, 0, 0, 2, 0, 1, 0, 6, 0, 2, 2, 0, 0, 0, 8, 0, 0, 0, 7, 6, 0, 2, 2, 24, 0, 6, 0, 2, 0, 0, 8, 6, 0, 1, 32, 0, 0, 2, 6, 6, 0, 0, 2, 32, 0, 0, 12, 30, 0, 2

Offset

0,14

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(25) = 3 because we have [25], [16, 9] and [9, 16].

Maple

b:= proc(n, i, p) option remember;
      `if`(n=0, p!, `if`(i*(i+1)*(2*i+1)/6-1<n, 0,
      `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..87);  # Alois P. Heinz, Feb 03 2020

Mathematica

b[n_, i_, p_] := b[n, i, p] = If[n == 0, p!, If[i(i+1)(2i+1)/6 - 1 < n, 0, If[i^2 > n, 0, b[n - i^2, i - 1, p + 1]] + b[n, i - 1, p]]];
a[n_] := b[n, Floor@Sqrt[n], 0];
a /@ Range[0, 87] (* Jean-François Alcover, Nov 26 2020, after Alois P. Heinz *)

Crossrefs

Cf. A000290, A006456, A032020, A032021, A032022, A033461, A078134, A280129, A280542, A331844, A331918.

Sequence in context: A109527 A362424 A186715 * A219485 A337165 A057918

Adjacent sequences: A331980 A331981 A331982 * A331984 A331985 A331986

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 03 2020

Status

approved