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A035641
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Number of partitions of n into parts 6k and 6k+5 with at least one part of each type.
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3
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 3, 0, 0, 0, 1, 3, 6, 0, 0, 1, 3, 7, 11, 0, 1, 3, 7, 14, 18, 1, 3, 7, 15, 25, 30, 3, 7, 15, 28, 44, 47, 7, 15, 29, 51, 72, 73, 15, 29, 54, 87, 116, 111, 29, 55, 94, 144, 180, 167, 55, 97, 159, 230, 276, 249, 98, 166, 259, 360
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OFFSET
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1,17
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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 + 5)))*(-1 + 1/Product_{k>=1} (1 - x^(6 k))). - Robert Price, Aug 12 2020
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MATHEMATICA
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nmax = 75; s1 = Range[1, nmax/6]*6; s2 = Range[0, nmax/6]*6 + 5;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 12 2020 *)
nmax = 75; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(6 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(6 k + 5)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 12 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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