A322798 Number of compositions (ordered partitions) of n into hexagonal numbers (A000384).

1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 9, 12, 16, 22, 29, 37, 47, 60, 77, 101, 133, 174, 226, 292, 376, 486, 632, 823, 1072, 1394, 1808, 2342, 3036, 3939, 5116, 6648, 8636, 11211, 14548, 18875, 24493, 31795, 41283, 53604, 69594, 90338, 117251, 152184, 197540

Offset

0,7

Links

Alois P. Heinz, Table of n, a(n) for n = 0..8828

Eric Weisstein's World of Mathematics, Hexagonal Number

Index entries for sequences related to compositions

Formula

G.f.: 1/(1 - Sum_{k>=1} x^(k*(2*k-1))).

Maple

h:= proc(n) option remember; `if`(n<1, 0, (t->
      `if`(t*(2*t-1)>n, t-1, t))(1+h(n-1)))
    end:
a:= proc(n) option remember; `if`(n=0, 1,
      add(a(n-i*(2*i-1)), i=1..h(n)))
    end:
seq(a(n), n=0..60);  # Alois P. Heinz, Dec 28 2018

Mathematica

nmax = 50; CoefficientList[Series[1/(1 - Sum[x^(k (2 k - 1)), {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A000384, A006456, A023361, A181324, A278949, A279279, A322799, A322800.

Sequence in context: A367637 A322853 A322801 * A085793 A281809 A143286

Adjacent sequences: A322795 A322796 A322797 * A322799 A322800 A322801

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 26 2018

Status

approved