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Number of 6-regular bipartitions of n.
5

%I #8 Oct 08 2024 11:10:21

%S 1,2,5,10,20,36,63,106,175,280,441,680,1034,1548,2290,3346,4840,6930,

%T 9837,13844,19337,26810,36925,50530,68741,92984,125113,167490,223155,

%U 295960,390825,513954,673214,878480,1142190,1479892,1911051,2459896,3156602

%N Number of 6-regular bipartitions of n.

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

%F 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

%p f:=(k,M) -> mul(1-q^(k*j),j=1..M);

%p LRBP := (L,M) -> (f(L,M)/f(1,M))^2;

%p S := L -> seriestolist(series(LRBP(L,80),q,60));

%p S(6);

%t 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 *)

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

%Y Cf. A219601.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Oct 19 2019