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Number of 3-regular bipartitions of n.
5

%I #10 Oct 08 2024 11:10:06

%S 1,2,5,8,16,26,44,68,108,162,245,356,521,740,1053,1468,2045,2804,3836,

%T 5184,6988,9326,12409,16376,21546,28154,36674,47492,61317,78764,

%U 100880,128628,163553,207134,261630,329288,413395,517316,645803,803844,998282

%N Number of 3-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) ~ exp(Pi*sqrt(8*n)/3) / (2^(3/4) * 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(3);

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

%K nonn

%O 0,2

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