A099170 Generalized Motzkin paths with no hills and 3-horizontal steps.

1, 0, 0, 1, 1, 1, 3, 5, 9, 17, 34, 64, 128, 251, 505, 1007, 2044, 4132, 8444, 17243, 35461, 72975, 150910, 312488, 649359, 1351478, 2820366, 5895019, 12348082, 25903960, 54438338, 114563999, 241461037, 509563657, 1076758140

Offset

0,7

Links

Fung Lam, Table of n, a(n) for n = 0..2900

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.: [1-x^3+2x^2-sqrt(1-2x^3+x^6-4x^2)]/[2x^2*(2+x^2-x^3)].

Recurrence: 2*(n+2)*a(n) = (n-7)*a(n-9) + (7-n)*a(n-8) + (19-4*n)*a(n-6) - (1+2*n)*a(n-5) + 4*(n-1)*a(n-4) + (5*n-8)*a(n-3) + (7*n-10)*a(n-2). - Fung Lam, Feb 03 2014

Crossrefs

Cf. A001003, A089372, A099171.

Sequence in context: A127904 A048578 A087312 * A251705 A351938 A018095

Adjacent sequences: A099167 A099168 A099169 * A099171 A099172 A099173

Keyword

nonn

Author

Ralf Stephan, Oct 09 2004

Status

approved