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A335602
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Number of 3-regular cubic partitions of n.
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1
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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
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OFFSET
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0,3
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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