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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS 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. 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 Adjacent sequences: A128758 A128759 A128760 * A128762 A128763 A128764 KEYWORD nonn AUTHOR Ralf Stephan, May 08 2007 EXTENSIONS More terms from Vladeta Jovovic, Oct 03 2007 STATUS approved

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Last modified April 1 13:29 EDT 2023. Contains 361695 sequences. (Running on oeis4.)