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A115276
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Number of partitions of {1,...,n} into block sizes not a multiple of 4.
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5
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1, 1, 2, 5, 14, 47, 173, 702, 3124, 14901, 76405, 417210, 2411466, 14731095, 94573911, 636575050, 4480990936, 32887804361, 251236573561, 1993395483746, 16397468177406, 139634290253907, 1229013163330947, 11166172488138322, 104593176077399652
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f.: exp(sinh(x)+(cosh(x)-cos(x))/2).
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, add(`if`(
irem(j, 4)=0, 0, binomial(n-1, j-1)*a(n-j)), j=1..n))
end:
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MATHEMATICA
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a[n_] := a[n] = If[n == 0, 1, Sum[If[Mod[j, 4] == 0, 0, Binomial[n - 1, j - 1]*a[n - j]], {j, 1, n}]]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jan 20 2016, after Alois P. Heinz *)
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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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