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A099170 Generalized Motzkin paths with no hills and 3-horizontal steps. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A018095 A003217

Adjacent sequences:  A099167 A099168 A099169 * A099171 A099172 A099173

KEYWORD

nonn

AUTHOR

Ralf Stephan, Oct 09 2004

STATUS

approved

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Last modified June 17 13:43 EDT 2021. Contains 345080 sequences. (Running on oeis4.)