A189076 Number of compositions of n that avoid the pattern 23-1.

1, 1, 2, 4, 8, 16, 31, 61, 118, 228, 440, 846, 1623, 3111, 5955, 11385, 21752, 41530, 79250, 151161, 288224, 549408, 1047034, 1995000, 3800662, 7239710, 13789219, 26261678, 50012275, 95237360, 181350695, 345315255, 657506300, 1251912618, 2383636280, 4538364446

Offset

0,3

Comments

Note that an exponentiation ^(-1) is missing in Example 4.4. The notation in Theorem 4.3 is complete.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

S. Heubach, T. Mansour and A. O. Munagi, Avoiding Permutation Patterns of Type (2,1) in Compositions, Online Journal of Analytic Combinatorics, 4 (2009).

Maple

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

Mathematica

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}]];
a /@ Range[0, 32] (* Jean-François Alcover, Apr 02 2020, after R. J. Mathar *)

Crossrefs

Cf. A189075, A189077.

Sequence in context: A006775 A104993 A223940 * A192656 A128761 A332726

Adjacent sequences: A189073 A189074 A189075 * A189077 A189078 A189079

Keyword

nonn

Author

N. J. A. Sloane, Apr 16 2011

Status

approved