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A128695 Number of compositions of n with parts in N which avoid the adjacent pattern 111. 6
1, 1, 2, 3, 7, 13, 24, 46, 89, 170, 324, 618, 1183, 2260, 4318, 8249, 15765, 30123, 57556, 109973, 210137, 401525, 767216, 1465963, 2801115, 5352275, 10226930, 19541236, 37338699, 71345449, 136324309, 260483548, 497722578, 951030367 (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 compositions, arXiv:math/0603285 [math.CO], 2006

FORMULA

G.f.: 1/(1-sum(i>=1, x^i*(1+x^i)/(1+x^i*(1+x^i)) ) ).

a(n) ~ c * d^n, where d=1.9107639262818041675000243699745706859615884029961947632387839..., c=0.4993008137128378086219448701860326113802027003939127932922782... - Vaclav Kotesovec, May 01 2014

MAPLE

b:= proc(n, t) option remember; `if`(n=0, 1, add(`if`(abs(t)<>j,

       b(n-j, j), `if`(t=-j, 0, b(n-j, -j))), j=1..n))

    end:

a:= n-> b(n, 0):

seq(a(n), n=0..40);  # Alois P. Heinz, Nov 23 2013

MATHEMATICA

nn=33; CoefficientList[Series[1/(1-Sum[(x^i+x^(2i))/(1+x^i+x^(2i)), {i, 1, nn}]), {x, 0, nn}], x] (* Geoffrey Critzer, Nov 23 2013 *)

CROSSREFS

Column k=0 of A232435.

Cf. A091616, A232432.

Sequence in context: A075058 A213968 A213967 * A024504 A256494 A088172

Adjacent sequences:  A128692 A128693 A128694 * A128696 A128697 A128698

KEYWORD

nonn

AUTHOR

Ralf Stephan, May 08 2007

STATUS

approved

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Last modified February 23 11:52 EST 2020. Contains 332159 sequences. (Running on oeis4.)