A339441 Number of compositions (ordered partitions) of n into an even number of distinct triangular numbers.

1, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 4, 0, 2, 0, 24, 2, 2, 0, 2, 26, 0, 2, 0, 26, 0, 28, 24, 0, 26, 24, 2, 2, 50, 2, 48, 0, 26, 26, 0, 48, 28, 72, 2, 26, 48, 4, 48, 48, 24, 74, 770, 2, 50, 48, 50, 26, 72, 720, 98, 74, 26, 74, 48, 770, 74, 768, 26, 122, 792, 72

Offset

0,5

Links

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

Index entries for sequences related to compositions

Index to sequences related to polygonal numbers

Example

a(20) = 24 because we have [10, 6, 3, 1] (24 permutations).

Maple

b:= proc(n, i, p) option remember; `if`(n=0, irem(1+p, 2)*p!, (t->
     `if`(t>n, 0, b(n, i+1, p)+b(n-t, i+1, p+1)))(i*(i+1)/2))
    end:
a:= n-> b(n, 1, 0):
seq(a(n), n=0..100);  # Alois P. Heinz, Dec 05 2020

Mathematica

b[n_, i_, p_] := b[n, i, p] = If[n == 0, Mod[1 + p, 2]*p!, With[{t = i(i+1)/2}, If[t > n, 0, b[n, i + 1, p] + b[n - t, 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. A000217, A331843, A332305, A339375, A339416, A339442.

Sequence in context: A035461 A118508 A029305 * A226914 A110036 A308046

Adjacent sequences: A339438 A339439 A339440 * A339442 A339443 A339444

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 05 2020

Status

approved