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 A099171 Generalized Motzkin paths with no hills and 4-horizontal steps (even coefficients). 2
 0, 2, 3, 12, 37, 132, 473, 1753, 6612, 25355, 98492, 386812, 1533269, 6126254, 24647539, 99766315, 405994556, 1660072482, 6816932349, 28101049860, 116243913509, 482387204447, 2007615713528, 8377621010483, 35044880237710 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Odd coefficients are zero. LINKS Fung Lam, Table of n, a(n) for n = 0..1500 E. Barcucci, E. Pergola, R. Pinzani and S. Rinaldi, ECO method and hill-free generalized Motzkin paths, SÃ©minaire Lotharingien de Combinatoire, B46b (2001), 14 pp. FORMULA 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)]. 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 CROSSREFS Cf. A001003, A089372, A099170. Sequence in context: A072440 A135522 A107240 * A268561 A012307 A012311 Adjacent sequences:  A099168 A099169 A099170 * A099172 A099173 A099174 KEYWORD nonn AUTHOR Ralf Stephan, Oct 09 2004 STATUS approved

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Last modified May 9 07:36 EDT 2021. Contains 343692 sequences. (Running on oeis4.)