A328545 Number of 11-regular partitions of n (no part is a multiple of 11).

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 55, 76, 99, 132, 171, 224, 286, 370, 468, 597, 750, 945, 1177, 1472, 1820, 2255, 2772, 3410, 4165, 5092, 6185, 7515, 9085, 10978, 13207, 15884, 19025, 22774, 27170, 32388, 38489, 45705, 54120, 64030, 75569, 89100

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(11);

Mathematica

Table[Count[IntegerPartitions@n, x_ /; ! MemberQ [Mod[x, 11], 0, 2] ], {n, 0, 46}]

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=11. - Vaclav Kotesovec, Aug 01 2022