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%I #26 Apr 02 2020 09:26:55
%S 1,1,2,4,8,16,31,61,118,228,440,846,1623,3111,5955,11385,21752,41530,
%T 79250,151161,288224,549408,1047034,1995000,3800662,7239710,13789219,
%U 26261678,50012275,95237360,181350695,345315255,657506300,1251912618,2383636280,4538364446
%N Number of compositions of n that avoid the pattern 23-1.
%C Note that an exponentiation ^(-1) is missing in Example 4.4. The notation in Theorem 4.3 is complete.
%H Alois P. Heinz, <a href="/A189076/b189076.txt">Table of n, a(n) for n = 0..300</a>
%H S. Heubach, T. Mansour and A. O. Munagi, <a href="https://web.math.rochester.edu/misc/ojac/vol4/CompType21.pdf">Avoiding Permutation Patterns of Type (2,1) in Compositions</a>, Online Journal of Analytic Combinatorics, 4 (2009).
%p A189075 := proc(n) local g,i; g := 1; for i from 1 to n do 1-x^i/mul ( 1-x^j,j=i+1..n-i) ; g := g*% ; end do: g := expand(1/g) ; g := taylor(g,x=0,n+1) ; coeftayl(g,x=0,n) ; end proc: # _R. J. Mathar_, Apr 16 2011
%t a[n_] := Module[{g = 1, xi}, Do[xi = 1 - x^i/Product[1 - x^j, {j, i+1, n-i}]; g = g xi, {i, n}]; SeriesCoefficient[1/g, {x, 0, n}]];
%t a /@ Range[0, 32] (* _Jean-François Alcover_, Apr 02 2020, after _R. J. Mathar_ *)
%Y Cf. A189075, A189077.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Apr 16 2011
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