A328548 - OEIS

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

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OFFSET

0,2

REFERENCES

Kathiravan, T., and S. N. Fathima. "On L-regular bipartitions modulo L." The Ramanujan Journal 44.3 (2017): 549-558.

LINKS

Table of n, a(n) for n=0..38.

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

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 *)

CROSSREFS

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

Cf. A219601.

Sequence in context: A365631 A117487 A263348 * A294536 A325650 A325720

Adjacent sequences: A328545 A328546 A328547 * A328549 A328550 A328551

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 19 2019

STATUS

approved