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A015755
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Number of partitions of n into distinct parts, none being 8.
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8
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1, 1, 1, 2, 2, 3, 4, 5, 5, 7, 9, 10, 13, 15, 18, 22, 27, 31, 37, 44, 51, 61, 71, 82, 95, 111, 128, 148, 171, 195, 225, 258, 295, 337, 384, 437, 497, 565, 639, 724, 818, 923, 1042, 1173, 1319, 1483, 1665, 1866, 2092, 2341, 2616, 2924, 3263, 3637, 4053, 4512, 5016
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = A000009(n) - a(n-8) for n >= 0, a(n) = 0 otherwise. - Yuchun Ji, Dec 25 2018
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MATHEMATICA
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CoefficientList[Series[Product[1+q^n, {n, 1, 60}]/(1+q^8), {q, 0, 60}], q]
Table[Count[Select[IntegerPartitions[n], DeleteDuplicates[#] == # &], x_ /; ! MemberQ[x, 8]], {n, 0, 56}] (* Robert Price, May 18 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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EXTENSIONS
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STATUS
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approved
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