A328548 Number of 6-regular bipartitions of n.

1, 2, 5, 10, 20, 36, 63, 106, 175, 280, 441, 680, 1034, 1548, 2290, 3346, 4840, 6930, 9837, 13844, 19337, 26810, 36925, 50530, 68741, 92984, 125113, 167490, 223155, 295960, 390825, 513954, 673214, 878480, 1142190, 1479892, 1911051, 2459896, 3156602

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.

Crossrefs

Number of r-regular bipartitions of n for r = 2,3,4,5,6: A022567, A328547, A001936, A263002, A328548.

Cf. A219601.

Programs

Maple

f:=(k,M) -> mul(1-q^(k*j),j=1..M);
LRBP := (L,M) -> (f(L,M)/f(1,M))^2;
S := L -> seriestolist(series(LRBP(L,80),q,60));
S(6);

Mathematica

nmax = 40; CoefficientList[Series[Product[(1 - x^(6*k))/(1 - x^k), {k, 1, nmax}]^2, {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 08 2024 *)

Formula

a(n) ~ 5^(1/4) * exp(Pi*sqrt(10*n)/3) / (2^(9/4) * 3^(3/2) * n^(3/4)). - Vaclav Kotesovec, Oct 08 2024