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A128761
Number of compositions of n with parts in N which avoid the consecutive pattern 123.
22
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
OFFSET
0,3
LINKS
S. Heubach and T. Mansour, Enumeration of 3-letter patterns in combinations, arXiv:math/0603285 [math.CO], 2006.
FORMULA
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
MAPLE
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
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A223940 A189076 A192656 * A332726 A239557 A001591
KEYWORD
nonn
AUTHOR
Ralf Stephan, May 08 2007
EXTENSIONS
More terms from Vladeta Jovovic, Oct 03 2007
STATUS
approved