A328547 - OEIS

A328547

Number of 3-regular bipartitions of n.

1, 2, 5, 8, 16, 26, 44, 68, 108, 162, 245, 356, 521, 740, 1053, 1468, 2045, 2804, 3836, 5184, 6988, 9326, 12409, 16376, 21546, 28154, 36674, 47492, 61317, 78764, 100880, 128628, 163553, 207134, 261630, 329288, 413395, 517316, 645803, 803844, 998282

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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..40.

FORMULA

a(n) ~ exp(Pi*sqrt(8*n)/3) / (2^(3/4) * 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(3);

MATHEMATICA

nmax = 40; CoefficientList[Series[Product[1 + x^j + x^(2*j), {j, 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. A000726.

Sequence in context: A171238 A096541 A226015 * A137685 A169826 A093065

Adjacent sequences: A328544 A328545 A328546 * A328548 A328549 A328550

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 19 2019

STATUS

approved