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A035671
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Number of partitions of n into parts 7k+5 and 7k+6 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, 1, 2, 0, 0, 1, 1, 3, 2, 3, 1, 1, 3, 3, 6, 5, 5, 3, 3, 7, 8, 11, 9, 8, 7, 9, 15, 15, 19, 16, 15, 16, 19, 27, 28, 32, 28, 27, 32, 36, 48, 48, 52, 49, 49, 58, 65, 80, 81, 85, 84, 84, 101, 111, 131, 132, 137, 138, 143, 169, 184, 208, 213
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OFFSET
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1,18
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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 + 5)))*(-1 + 1/Product_{k>=0} (1 - x^(7 k + 6). - Robert Price, Aug 15 2020
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MATHEMATICA
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nmax = 78; s1 = Range[0, nmax/7]*7 + 5; s2 = Range[0, nmax/7]*7 + 6;
Table[Count[IntegerPartitions[n, All, s1~Join~s2],
x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* Robert Price, Aug 15 2020 *)
nmax = 78; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(7 k + 5)), {k, 0, nmax}])*(-1 + 1/Product[(1 - x^(7 k + 6)), {k, 0, nmax}]), {x, 0, nmax}], x] (* Robert Price, Aug 15 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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