A339430 Number of compositions (ordered partitions) of n into an even number of distinct squares.

1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 24, 0, 0, 0, 2, 0, 0, 2, 0, 24, 2, 2, 0, 0, 0, 2, 24, 0, 0, 0, 26, 24, 2, 2, 24, 0, 0, 24, 2, 0, 0, 2, 24, 24, 0, 28, 24, 0, 2, 0, 24, 24, 0, 2, 26, 24, 0, 0, 72, 24, 2

Offset

0,6

Links

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

Index entries for sequences related to compositions

Index entries for sequences related to sums of squares

Example

a(30) = 24 because we have [16, 9, 4, 1] (24 permutations).

Maple

b:= proc(n, i, p) option remember; `if`(n=0, irem(1+p, 2)*p!,
     (s-> `if`(s>n, 0, b(n, i+1, p)+b(n-s, i+1, p+1)))(i^2))
    end:
a:= n-> b(n, 1, 0):
seq(a(n), n=0..100);  # Alois P. Heinz, Dec 04 2020

Mathematica

b[n_, i_, p_] := b[n, i, p] = If[n == 0, Mod[1 + p, 2]*p!,
     With[{s = i^2}, If[s > n, 0, b[n, i + 1, p] +
     b[n - s, i + 1, p + 1]]]];
a[n_] := b[n, 1, 0];
a /@ Range[0, 100] (* Jean-François Alcover, Mar 09 2021, after Alois P. Heinz *)

Crossrefs

Cf. A000290, A331844, A332305, A339366, A339418, A339431.

Sequence in context: A022882 A171919 A000089 * A350386 A352550 A348326

Adjacent sequences: A339427 A339428 A339429 * A339431 A339432 A339433

Keyword

nonn,look

Author

Ilya Gutkovskiy, Dec 04 2020

Status

approved