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A128742 Number of compositions of n with parts in N which avoid the pattern 112. 4
1, 1, 2, 4, 7, 13, 24, 43, 78, 142, 256, 463, 838, 1513, 2735, 4944, 8931, 16139, 29164, 52693, 95213, 172042, 310855, 561682, 1014898, 1833794, 3313454, 5987026, 10817836, 19546558, 35318325, 63816013, 115307993, 208347899, 376459955, 680218580, 1229074432 (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

G.f.: 1/( 1 - Sum_{j>=1} x^j*Product_{i=1..j-1} (1-x^(2*i)) ).

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, 0):

seq(a(n), n=0..40);  # 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, 0];

Table[a[n], {n, 0, 40}] (* Jean-Fran├žois Alcover, Nov 06 2017, after Alois P. Heinz *)

CROSSREFS

Sequence in context: A049284 A049285 A002843 * A318748 A107281 A006744

Adjacent sequences:  A128739 A128740 A128741 * A128743 A128744 A128745

KEYWORD

nonn

AUTHOR

Ralf Stephan, May 08 2007

STATUS

approved

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Last modified January 25 01:42 EST 2020. Contains 331229 sequences. (Running on oeis4.)