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A188900 Number of compositions of n that avoid the pattern 12-3. 2

%I #30 Oct 22 2022 14:59:55

%S 1,1,2,4,8,16,31,60,114,215,402,746,1375,2520,4593,8329,15036,27027,

%T 48389,86314,153432,271853,480207,845804,1485703,2603018,4549521,

%U 7933239,13803293,23966682,41530721,71830198,124010381,213725823,367736268,631723139,1083568861

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

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

%H Nathaniel Johnston, <a href="/A188900/b188900.txt">Table of n, a(n) for n = 0..200</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).

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

%p 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);

%t m = 35;

%t Product[1/(1 - x^i/Product[1 - x^j, {j, 1, i - 1}]), {i, 1, m}] + O[x]^m // CoefficientList[#, x]& (* _Jean-Fran├žois Alcover_, Mar 31 2020 *)

%Y Cf. A189076, A189077.

%K nonn

%O 0,3

%A _Nathaniel Johnston_, Apr 17 2011

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Last modified March 5 08:40 EST 2024. Contains 370538 sequences. (Running on oeis4.)