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A035658
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Number of partitions of n into parts 7k+1 and 7k+3 with at least one part of each type.
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3
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0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 5, 5, 6, 8, 8, 9, 11, 14, 16, 18, 22, 24, 26, 30, 36, 40, 45, 53, 57, 62, 71, 80, 89, 100, 114, 124, 135, 151, 167, 184, 205, 229, 249, 271, 299, 327, 358, 395, 436, 474, 515, 564, 612, 666, 730, 798, 864, 937, 1019, 1100, 1192, 1298
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OFFSET
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1,7
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LINKS
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FORMULA
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G.f.: (-1 + 1/Product_{k>=0} (1 - x^(7 k + 1)))*(-1 + 1/Product_{k>=0} (1 - x^(7 k + 3))). - Robert Price, Aug 16 2020
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MATHEMATICA
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nmax = 62; s1 = Range[0, nmax/7]*7 + 1; s2 = Range[0, nmax/7]*7 + 3;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 14 2020 *)
nmax = 62; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k + 1)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(7 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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