A294621 Number of partitions of n into generalized heptagonal numbers (A085787).

1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 18, 20, 21, 23, 26, 29, 32, 35, 38, 41, 45, 49, 53, 59, 64, 69, 73, 80, 87, 94, 101, 109, 117, 125, 134, 145, 156, 167, 178, 190, 202, 217, 232, 249, 265, 282, 299, 318, 339, 361, 384, 408, 432, 457, 484, 514, 545, 578, 610, 646

Offset

0,5

Links

Table of n, a(n) for n=0..70.

Eric Weisstein's World of Mathematics, Heptagonal Number

Index to sequences related to polygonal numbers

Index entries for related partition-counting sequences

Formula

G.f.: Product_{k>=1} 1/((1 - x^(k*(5*k-3)/2))*(1 - x^(k*(5*k+3)/2))).

Example

a(8) = 4 because we have [7, 1], [4, 4], [4, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1].

Mathematica

nmax = 70; CoefficientList[Series[Product[1/((1 - x^(k (5 k - 3)/2)) (1 - x^(k (5 k + 3)/2))), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A007294, A085787, A095699, A279012, A294622, A294623.

Sequence in context: A025773 A308303 A285763 * A029077 A112176 A112205

Adjacent sequences: A294618 A294619 A294620 * A294622 A294623 A294624

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 05 2017

Status

approved