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

0,3

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

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

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}]

Crossrefs

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

Sequence in context: A238868 A035999 A036010 * A192061 A218511 A008640

Adjacent sequences: A328542 A328543 A328544 * A328546 A328547 A328548

Keyword

nonn

Author

N. J. A. Sloane, Oct 19 2019

Status

approved