A331919 Number of compositions (ordered partitions) of n into distinct tetrahedral numbers.

1, 1, 0, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 0, 2, 6, 0, 0, 0, 0, 1, 2, 0, 0, 2, 6, 0, 0, 0, 0, 2, 6, 0, 0, 6, 25, 2, 0, 0, 2, 6, 0, 0, 0, 0, 2, 6, 0, 0, 6, 24, 0, 0, 0, 0, 2, 7, 2, 0, 6, 26, 6, 0, 0, 0, 6, 26, 6, 0, 24, 126, 24, 0, 0, 0, 0, 2, 6, 0, 0, 6, 24, 0, 0, 1, 2, 6, 24, 2, 6, 24

Offset

0,6

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Index entries for sequences related to compositions

Example

a(15) = 6 because we have [10, 4, 1], [10, 1, 4], [4, 10, 1], [4, 1, 10], [1, 10, 4] and [1, 4, 10].

Maple

N:= 200: # for a(0)..a(N)
G:= mul(1+t*x^(i*(i+1)*(i+2)/6), i=1..floor((6*N)^(1/3))):
F:= proc(n) local R, k, v;
  R:= coeff(G, x, n);
  add(k!*coeff(R, t, k), k=1..degree(R, t))
end proc:
F(0):= 1:
map(F, [$0..N]); # Robert Israel, Feb 03 2020

Mathematica

M = 100;
G = Product[1 + t x^(i(i+1)(i+2)/6), {i, 1, Floor[(6M)^(1/3)]}];
F[n_] := Module[{R, k, v}, R = Coefficient[G, x, n]; Sum[k! Coefficient[R, t, k], {k, 1, Exponent[R, t]}]];
F[0] = 1;
F /@ Range[0, M] (* Jean-François Alcover, Jun 20 2020, after Robert Israel *)

Crossrefs

Cf. A000292, A023361, A068980, A279278, A282582, A298857, A331843, A331984.

Sequence in context: A339088 A025907 A024157 * A332005 A039968 A092037

Adjacent sequences: A331916 A331917 A331918 * A331920 A331921 A331922

Keyword

nonn,look

Author

Ilya Gutkovskiy, Feb 01 2020

Status

approved