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 A188900 Number of compositions of n that avoid the pattern 12-3. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 4 01:51 EST 2023. Contains 367541 sequences. (Running on oeis4.)