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A335746
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a(n) is the number of partitions of n into distinct parts such that the number of parts divisible by 3 is even.
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0
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1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 8, 9, 11, 14, 16, 19, 23, 27, 32, 38, 45, 52, 61, 71, 83, 96, 111, 128, 148, 170, 195, 224, 256, 293, 334, 380, 432, 491, 557, 630, 713, 805, 908, 1024, 1152, 1295, 1455, 1632, 1829, 2049, 2291, 2560, 2859, 3189, 3554, 3959, 4404, 4896, 5440
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OFFSET
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0,6
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LINKS
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FORMULA
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G.f.: 1/2*(Product_{n>=1} (1+q^n) + Product_{n>=1} (1+q^(3*n-2))*(1+q^(3*n-1))*(1-q^(3*n))).
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EXAMPLE
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a(10) = 5, the relevant partitions of 10 into distinct parts being [10], [8,2], [7,2,1], [6,3,1], [5,4,1].
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PROG
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(PARI) seq(n)={my(A=O(x*x^n)); Vec(prod(k=1, n, 1 + x^k + A) + prod(k=1, ceil(n/3), (1+x^(3*k-2)+A)*(1+x^(3*k-1)+A)*(1-x^(3*k)+A)))/2} \\ Andrew Howroyd, Jul 02 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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