A328546 Number of 12-regular partitions of n (no part is a multiple of 12).

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 76, 100, 133, 173, 226, 290, 374, 475, 605, 762, 960, 1199, 1497, 1856, 2299, 2831, 3482, 4261, 5208, 6337, 7700, 9321, 11266, 13572, 16325, 19578, 23444, 27999, 33389, 39721, 47185, 55929, 66199, 78199, 92246

Offset: 0

Author

N. J. A. Sloane, Oct 19 2019

Keywords

• nonn

References

• Kathiravan, T., and S. N. Fathima. "On L-regular bipartitions modulo L." The Ramanujan Journal 44.3 (2017): 549-558.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Number of r-regular partitions for r = 2 through 12: A000009, A000726, A001935, A035959, A219601, A035985, A261775, A104502, A261776, A328545, A328546.

Programs

Maple

f:=(k,M) -> mul(1-q^(k*j),j=1..M);
LRP := (L,M) -> f(L,M)/f(1,M);
s := L -> seriestolist(series(LRP(L,80),q,60));
s(12);

Mathematica

Table[Count[IntegerPartitions@n, x_ /; ! MemberQ [Mod[x, 12], 0, 2] ], {n, 0, 46}] (* Robert Price, Jul 28 2020 *)

Formula

a(n) ~ exp(Pi*sqrt(2*n*(s-1)/(3*s))) * (s-1)^(1/4) / (2 * 6^(1/4) * s^(3/4) * n^(3/4)) * (1 + ((s-1)^(3/2)*Pi/(24*sqrt(6*s)) - 3*sqrt(6*s) / (16*Pi * sqrt(s-1))) / sqrt(n) + ((s-1)^3*Pi^2/(6912*s) - 45*s/(256*(s-1)*Pi^2) - 5*(s-1)/128) / n), set s=12. - Vaclav Kotesovec, Aug 01 2022