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A128761
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Number of compositions of n with parts in N which avoid the consecutive pattern 123.
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22
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1, 1, 2, 4, 8, 16, 31, 61, 119, 232, 453, 883, 1721, 3354, 6536, 12735, 24813, 48344, 94189, 183506, 357518, 696534, 1357019, 2643798, 5150746, 10034865, 19550268, 38088486, 74205248, 144569092, 281654211, 548727863, 1069049370, 2082756500
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OFFSET
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0,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..1000
S. Heubach and T. Mansour, Enumeration of 3-letter patterns in combinations, arXiv:math/0603285 [math.CO], 2006.
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FORMULA
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The Heubach/Mansour paper has a complicated g.f.
a(n) ~ c * d^n, where d = 1.948232199887283224240693518762976752988220177086321158242512704029011807341..., c = 0.57609601848694597639954632728322472031509789101742496394456882851645843... - Vaclav Kotesovec, Sep 20 2019
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MAPLE
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b:= proc(n, t, l) option remember; `if`(n=0, 1, add(
b(n-j, is(j>l), j), j=1..min(n, `if`(t, l, n))))
end:
a:= n-> b(n, false, n):
seq(a(n), n=0..35); # Alois P. Heinz, Oct 24 2017
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MATHEMATICA
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b[n_, t_, l_] := b[n, t, l] = If[n == 0, 1, Sum[b[n - j, j > l, j], {j, 1, Min[n, If[t, l, n]]}]];
a[n_] := b[n, False, n];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Nov 14 2017, after Alois P. Heinz *)
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CROSSREFS
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Sequence in context: A223940 A189076 A192656 * A332726 A239557 A001591
Adjacent sequences: A128758 A128759 A128760 * A128762 A128763 A128764
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan, May 08 2007
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EXTENSIONS
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More terms from Vladeta Jovovic, Oct 03 2007
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STATUS
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approved
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