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 A099171 Generalized Motzkin paths with no hills and 4-horizontal steps (even coefficients). 2

%I

%S 0,2,3,12,37,132,473,1753,6612,25355,98492,386812,1533269,6126254,

%T 24647539,99766315,405994556,1660072482,6816932349,28101049860,

%U 116243913509,482387204447,2007615713528,8377621010483,35044880237710

%N Generalized Motzkin paths with no hills and 4-horizontal steps (even coefficients).

%C Odd coefficients are zero.

%H Fung Lam, <a href="/A099171/b099171.txt">Table of n, a(n) for n = 0..1500</a>

%H E. Barcucci, E. Pergola, R. Pinzani and S. Rinaldi, <a href="http://www.mat.univie.ac.at/~slc/wpapers/s46rinaldi.html">ECO method and hill-free generalized Motzkin paths</a>, SÃ©minaire Lotharingien de Combinatoire, B46b (2001), 14 pp.

%F G.f.: Sum[n>=0, a(n)x^(2n)] = [1-x^4+2x^2-sqrt(1-2x^4+x^8-4x^2)]/[2x^2*(2+x^2-x^4)].

%F Recurrence: 2*(n+10)*a(n) = (n-2)*a(n-6) + (2-n)*a(n-5) - 4*(n+1)*a(n-4) - 2*(n+10)*a(n-3) + 9*(n+6)*a(n-2) + (7*n+46)*a(n-1), where n >= 6 and is even. - _Fung Lam_, Feb 03 2014

%Y Cf. A001003, A089372, A099170.

%K nonn

%O 0,2

%A _Ralf Stephan_, Oct 09 2004

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Last modified June 17 00:17 EDT 2021. Contains 345080 sequences. (Running on oeis4.)