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

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. A000726.

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(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 *)

Formula

a(n) ~ exp(Pi*sqrt(8*n)/3) / (2^(3/4) * 3^(3/2) * n^(3/4)). - Vaclav Kotesovec, Oct 08 2024