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

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

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, Séminaire 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: A135522 A353831 A107240 * A268561 A352099 A012307

Adjacent sequences: A099168 A099169 A099170 * A099172 A099173 A099174

Keyword

nonn

Author

Ralf Stephan, Oct 09 2004

Status

approved