A294623 Number of partitions of n into distinct generalized heptagonal numbers (A085787).

1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 0, 2, 3, 1, 0, 3, 3, 1, 2, 2, 1, 1, 3, 3, 3, 2, 1, 2, 3, 4, 3, 2, 2, 3, 3, 3, 5, 3, 1, 3, 4, 3, 4, 5, 2, 3, 5, 4, 3, 4, 5, 4, 4, 3, 5, 5, 3, 5, 7, 5, 3, 6, 6, 6, 6, 5, 5, 6, 6, 5, 8, 7, 5, 5, 6, 7, 8, 8

Offset

0,19

Links

Table of n, a(n) for n=0..100.

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 + x^(k*(5*k-3)/2))*(1 + x^(k*(5*k+3)/2)).

Example

a(18) = 2 because we have [18] and [13, 4, 1].

Mathematica

nmax = 100; CoefficientList[Series[Product[(1 + x^(k (5 k - 3)/2)) (1 + x^(k (5 k + 3)/2)), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A024940, A085787, A279280, A290942, A294621, A294624.

Sequence in context: A284582 A120336 A284558 * A337473 A039738 A191515

Adjacent sequences: A294620 A294621 A294622 * A294624 A294625 A294626

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 05 2017

Status

approved