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A199884
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Number of compositions of n such that the number of parts is not divisible by the greatest part.
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2
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0, 1, 1, 6, 8, 19, 43, 90, 167, 339, 722, 1503, 2987, 5883, 11820, 24167, 49348, 99707, 199626, 398475, 797457, 1604029, 3237867, 6534327, 13143278, 26336266, 52664325, 105349525, 211135006, 423949168, 851981311, 1711365899, 3433202397, 6878160656, 13768314357
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OFFSET
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1,4
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..250
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FORMULA
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G.f.: Sum_{n>0} (2^(n-1)*x^n -Sum_{d|n} ((x^(d+1)-x)^n-(x^d-x)^n)/(x-1)^n).
a(n) = A000079(n-1) - A171634(n).
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EXAMPLE
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a(5) = 8: [1,2,2], [1,4], [2,1,2], [2,2,1], [2,3], [3,2], [4,1], [5].
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MAPLE
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b:= proc(n, t, g) option remember; `if` (n=0, `if` (irem(t, g)=0, 0, 1), add (b(n-i, t+1, max(i, g)), i=1..n)) end: a:= n-> b(n, 0, 0): seq (a(n), n=1..40);
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CROSSREFS
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Cf. A000079, A171634, A200727.
Sequence in context: A022542 A108341 A173975 * A028331 A113806 A105775
Adjacent sequences: A199881 A199882 A199883 * A199885 A199886 A199887
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Nov 11 2011
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STATUS
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approved
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