A339431 Number of compositions (ordered partitions) of n into an odd number of distinct squares.

0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 6, 0, 1, 0, 0, 0, 0, 6, 0, 0, 0, 1, 6, 0, 0, 6, 6, 0, 0, 0, 0, 6, 1, 0, 6, 0, 0, 6, 6, 0, 0, 6, 6, 0, 0, 7, 6, 0, 0, 6, 6, 120, 6, 0, 0, 6, 0, 6, 12, 0, 1, 6, 126, 0, 0, 12, 6, 0, 0, 0, 12, 126, 0, 12, 6, 120, 0, 7

Offset

0,15

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(55) = 120 because we have [25, 16, 9, 4, 1] (120 permutations).

Maple

b:= proc(n, i, p) option remember; `if`(n=0, irem(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[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 14 2021, after Alois P. Heinz *)

Crossrefs

Cf. A000290, A331844, A332304, A339367, A339419, A339430.

Sequence in context: A192072 A060297 A240315 * A256041 A137378 A333275

Adjacent sequences: A339428 A339429 A339430 * A339432 A339433 A339434

Keyword

nonn,look

Author

Ilya Gutkovskiy, Dec 04 2020

Status

approved