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A035646
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Number of partitions of n into parts 6k+2 and 6k+3 with at least one part of each type.
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3
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0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 4, 1, 4, 4, 4, 4, 10, 4, 11, 11, 11, 12, 22, 12, 25, 25, 26, 28, 45, 29, 52, 52, 55, 60, 87, 63, 101, 102, 108, 118, 160, 126, 187, 189, 202, 221, 285, 238, 333, 338, 363, 395, 492, 430, 574, 585, 629, 684, 828, 749, 964, 987, 1061
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OFFSET
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1,11
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LINKS
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FORMULA
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G.f.: (-1 + 1/Product_{k>=0} (1 - x^(6 k + 2)))*(-1 + 1/Product_{k>=0} (1 - x^(6 k + 3))). - Robert Price, Aug 16 2020
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MATHEMATICA
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nmax = 63; s1 = Range[0, nmax/6]*6 + 2; s2 = Range[0, nmax/6]*6 + 3;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 13 2020 *)
nmax = 63; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k + 2)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 3)), {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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