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A035619
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Number of partitions of n into parts 3k and 3k+2 with at least one part of each type.
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4
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0, 0, 0, 0, 1, 0, 1, 3, 1, 3, 7, 3, 8, 14, 8, 17, 26, 18, 33, 47, 36, 61, 81, 68, 106, 137, 121, 181, 224, 209, 296, 362, 347, 478, 570, 565, 750, 890, 894, 1166, 1360, 1396, 1774, 2062, 2134, 2677, 3076, 3228, 3973, 4555, 4804, 5854, 6657, 7085, 8513
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OFFSET
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1,8
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LINKS
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FORMULA
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G.f.: (-1 + 1/Product_{k>=1} (1 - x^(3 k)))*(-1 + 1/Product_{k>=0} (1 - x^(3 k + 2))). - Robert Price, Aug 16 2020
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MATHEMATICA
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nmax = 55; s1 = Range[1, nmax/3]*3; s2 = Range[0, nmax/3]*3 + 2;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 06 2020 *)
nmax = 55; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(3 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(3 k + 2)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 16 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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