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A335602
Number of 3-regular cubic partitions of n.
1
1, 1, 3, 3, 8, 9, 17, 20, 36, 43, 70, 84, 131, 158, 234, 284, 408, 495, 690, 837, 1143, 1385, 1852, 2241, 2952, 3565, 4626, 5574, 7150, 8595, 10903, 13074, 16434, 19656, 24494, 29223, 36146, 43016, 52836, 62722, 76572, 90675, 110063, 130021, 157014, 185049, 222388
OFFSET
0,3
LINKS
S. Chern, Arithmetic Properties for Cubic Partition Pairs Modulo Powers of 3, Acta. Math. Sin.-English Ser. 2017 33: 1504.
D. S. Gireesh and M. S. Mahadeva Naika, General family of congruences modulo large powers of 3 for cubic partition pairs, New Zealand J. Math. 47 (2017), 43--56.
FORMULA
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)).
a(n) ~ exp(sqrt(2*n/3)*Pi) / (6^(5/4) * n^(3/4)). - Vaclav Kotesovec, Jun 23 2020
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Sequence in context: A135477 A182473 A363125 * A092549 A260890 A022663
KEYWORD
nonn
AUTHOR
STATUS
approved