|
%I #13 Aug 01 2022 06:49:02
%S 1,1,2,3,5,7,11,15,22,30,42,56,76,100,133,173,226,290,374,475,605,762,
%T 960,1199,1497,1856,2299,2831,3482,4261,5208,6337,7700,9321,11266,
%U 13572,16325,19578,23444,27999,33389,39721,47185,55929,66199,78199,92246
%N Number of 12-regular partitions of n (no part is a multiple of 12).
%D Kathiravan, T., and S. N. Fathima. "On L-regular bipartitions modulo L." The Ramanujan Journal 44.3 (2017): 549-558.
%H Seiichi Manyama, <a href="/A328546/b328546.txt">Table of n, a(n) for n = 0..10000</a>
%F 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
%p f:=(k,M) -> mul(1-q^(k*j),j=1..M);
%p LRP := (L,M) -> f(L,M)/f(1,M);
%p s := L -> seriestolist(series(LRP(L,80),q,60));
%p s(12);
%t Table[Count[IntegerPartitions@n, x_ /; ! MemberQ [Mod[x, 12], 0, 2] ], {n, 0, 46}] (* _Robert Price_, Jul 28 2020 *)
%Y Number of r-regular partitions for r = 2 through 12: A000009, A000726, A001935, A035959, A219601, A035985, A261775, A104502, A261776, A328545, A328546.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Oct 19 2019
|
