A346798 Number of partitions of n into parts congruent to 0, 3 or 4 (mod 7).

1, 0, 0, 1, 1, 0, 1, 2, 1, 1, 3, 3, 2, 3, 6, 4, 4, 8, 9, 6, 10, 15, 12, 12, 21, 22, 18, 25, 36, 30, 32, 48, 52, 45, 60, 78, 72, 75, 105, 113, 105, 130, 166, 156, 166, 218, 236, 224, 274, 332, 325, 345, 436, 469, 462, 544, 649, 644, 688, 839, 907, 903, 1051

Offset

0,8

Links

Ludovic Schwob, Table of n, a(n) for n = 0..10000

Formula

G.f.: Product_{k>=1} 1/((1 - x^(7*k))*(1 - x^(7*k-3))*(1 - x^(7*k-4))).

a(n) = a(n-3) + a(n-4) - a(n-13) - a(n-15) + + - - (with a(0)=1 and a(n) = 0 for negative n), where 3, 4, 13, 15, ... is the sequence A057570.

a(n) ~ exp(Pi*sqrt(2*n/7)) / (8*cos(Pi/14)*n). - Vaclav Kotesovec, Aug 05 2021

Example

For n=19 the a(19)=6 solutions are 3+3+3+3+3+4, 3+3+3+3+7, 3+3+3+10, 3+4+4+4+4, 4+4+4+7, and 4+4+11.

Mathematica

CoefficientList[Series[Product[1/((1 - x^(7*k))(1 - x^(7*k-3))(1 - x^(7*k-4))), {k, 55}], {x, 0, 55}], x] (* Stefano Spezia, Aug 04 2021 *)

Crossrefs

Cf. A000041, A047342, A057570, A006950, A036820, A036822, A195848, A035363, A195849, A346797.

Sequence in context: A247749 A247367 A305321 * A340274 A127838 A017817

Adjacent sequences: A346795 A346796 A346797 * A346799 A346800 A346801

Keyword

nonn

Author

Ludovic Schwob, Aug 04 2021

Status

approved