A188900 Number of compositions of n that avoid the pattern 12-3.

1, 1, 2, 4, 8, 16, 31, 60, 114, 215, 402, 746, 1375, 2520, 4593, 8329, 15036, 27027, 48389, 86314, 153432, 271853, 480207, 845804, 1485703, 2603018, 4549521, 7933239, 13803293, 23966682, 41530721, 71830198, 124010381, 213725823, 367736268, 631723139, 1083568861

Offset

0,3

Comments

The value a(11) = 7464 in Heubach et al. is a typo.

Links

Nathaniel Johnston, Table of n, a(n) for n = 0..200

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

Formula

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

Maple

with(PolynomialTools):n:=20:taypoly:=taylor(mul(1/(1 - x^i/mul(1-x^j, j=1..i-1)), i=1..n), x=0, n+1):seq(coeff(taypoly, x, m), m=0..n);

Mathematica

m = 35;
Product[1/(1 - x^i/Product[1 - x^j, {j, 1, i - 1}]), {i, 1, m}] + O[x]^m // CoefficientList[#, x]& (* Jean-François Alcover, Mar 31 2020 *)

Crossrefs

Cf. A189076, A189077.

Sequence in context: A362063 A309982 A102726 * A189075 A345372 A189077

Adjacent sequences: A188897 A188898 A188899 * A188901 A188902 A188903

Keyword

nonn

Author

Nathaniel Johnston, Apr 17 2011

Status

approved