cp's OEIS Frontend

A335602 Number of 3-regular cubic partitions of n.

%I A335602 #34 Oct 27 2022 10:13:44
%S A335602 1,1,3,3,8,9,17,20,36,43,70,84,131,158,234,284,408,495,690,837,1143,
%T A335602 1385,1852,2241,2952,3565,4626,5574,7150,8595,10903,13074,16434,19656,
%U A335602 24494,29223,36146,43016,52836,62722,76572,90675,110063,130021,157014,185049,222388
%N A335602 Number of 3-regular cubic partitions of n.
%H A335602 H.-C. 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 A335602 H.-C. 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 A335602 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 A335602 D. S. Gireesh and M. S. Mahadeva Naika, <a href="https://www.thebookshelf.auckland.ac.nz/document.php?wid=4231">General family of congruences modulo large powers of 3 for cubic partition pairs</a>, New Zealand J. Math. 47 (2017), 43--56.
%F A335602 G.f.: (f_3(x)*f_6(x)) / (f_1(x)*f_2(x)) where f_k(x) = Product_{m>=1} (1 - x^(m*k)).
%F A335602 a(n) ~ exp(sqrt(2*n/3)*Pi) / (6^(5/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 23 2020
%t A335602 nmax = 20; CoefficientList[Series[Product[(1 - x^(3*k)) * (1 - x^(6*k)) / ((1 - x^k) * (1 - x^(2*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 23 2020 *)
%o A335602 (PARI) seq(n)={my(A=O(x*x^n)); Vec(eta(x^3 + A)*eta(x^6 + A)/(eta(x + A)*eta(x^2 + A)))} \\ _Andrew Howroyd_, Jul 29 2020
%Y A335602 Cf. A002513, A335604.
%K A335602 nonn
%O A335602 0,3
%A A335602 _Chandrappa Shivashankar_, Jun 15 2020