cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A335604 Number of 9-regular cubic partitions of n.

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%I A335604 #30 Oct 03 2020 03:00:44
%S A335604 1,1,3,4,9,12,23,31,54,72,117,156,242,320,477,628,909,1188,1676,2178,
%T A335604 3012,3888,5283,6780,9079,11582,15309,19424,25389,32040,41462,52063,
%U A335604 66780,83448,106182,132084,166862,206660,259359,319896,399069,490272,608234,744444,918864
%N A335604 Number of 9-regular cubic partitions of n.
%H A335604 Hei-Chi Chan, <a href="https://doi.org/10.1142/S1793042110003150">Ramanujan's cubic continued fraction and a generalization of his "most beautiful identity"</a>, Int. J. Number Theory 6 (2010), 673--680.
%H A335604 Hei-Chi Chan, <a href="https://doi.org/10.1142/S1793042110003241">Ramanujan's cubic continued fraction and Ramanujan type congruences for a certain partition function</a>,  Int. J. Number Theory  6 (2010), 819--834.
%H A335604 S. Chern, <a href="https://doi.org/10.1007/s10114-017-7052-z">Arithmetic Properties for Cubic Partition Pairs Modulo Powers of 3</a>, Acta. Math. Sin.-English Ser. 2017 33: 1504.
%H A335604 Bernard L. S. Lin, <a href="https://doi.org/10.1016/j.jnt.2016.07.012">Congruences modulo 27 for cubic partition pairs</a>, J. Number Theory 171 (2017), 31--42.
%F A335604 G.f.: (f_9(x)*f_18(x)) / (f_1(x)*f_2(x)) where f_k(x) = Product_{m>=1} (1 - x^(m*k)).
%F A335604 a(n) ~ exp(2*sqrt(2*n)*Pi/3) / (2^(3/4) * 3^(5/2) * n^(3/4)). - _Vaclav Kotesovec_, Jun 23 2020
%t A335604 nmax = 50; CoefficientList[Series[Product[(1 - x^(9*k)) * (1 - x^(18*k)) / ((1 - x^k) * (1 - x^(2*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 23 2020 *)
%o A335604 (PARI) seq(n)={my(A=O(x*x^n)); Vec(eta(x^9 + A)*eta(x^18 + A)/(eta(x + A)*eta(x^2 + A)))} \\ _Andrew Howroyd_, Jul 29 2020
%Y A335604 Cf. A002513, A335602.
%K A335604 nonn
%O A335604 0,3
%A A335604 _Chandrappa Shivashankar_, Jun 15 2020