cp's OEIS Frontend

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

%I A328545 #14 Aug 01 2022 06:48:52
%S A328545 1,1,2,3,5,7,11,15,22,30,42,55,76,99,132,171,224,286,370,468,597,750,
%T A328545 945,1177,1472,1820,2255,2772,3410,4165,5092,6185,7515,9085,10978,
%U A328545 13207,15884,19025,22774,27170,32388,38489,45705,54120,64030,75569,89100
%N A328545 Number of 11-regular partitions of n (no part is a multiple of 11).
%D A328545 Kathiravan, T., and S. N. Fathima. "On L-regular bipartitions modulo L." The Ramanujan Journal 44.3 (2017): 549-558.
%H A328545 Seiichi Manyama, <a href="/A328545/b328545.txt">Table of n, a(n) for n = 0..10000</a>
%F A328545 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
%p A328545 f:=(k,M) -> mul(1-q^(k*j),j=1..M);
%p A328545 LRP := (L,M) -> f(L,M)/f(1,M);
%p A328545 s := L -> seriestolist(series(LRP(L,80),q,60));
%p A328545 s(11);
%t A328545 Table[Count[IntegerPartitions@n, x_ /; ! MemberQ [Mod[x, 11], 0, 2] ], {n, 0, 46}]
%Y A328545 Number of r-regular partitions for r = 2 through 12: A000009, A000726, A001935, A035959, A219601, A035985, A261775, A104502, A261776, A328545, A328546.
%K A328545 nonn
%O A328545 0,3
%A A328545 _N. J. A. Sloane_, Oct 19 2019