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A099171 Generalized Motzkin paths with no hills and 4-horizontal steps (even coefficients). 1
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; internal format)
OFFSET

0,2

COMMENTS

Odd coefficients are zero.

LINKS

E. Barcucci, E. Pergola, R. Pinzani and S. Rinaldi, ECO method and hill-free generalized Motzkin paths

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)].

CROSSREFS

Cf. A001003, A089372, A099170.

Sequence in context: A072440 A135522 A107240 * A012307 A012311 A012513

Adjacent sequences:  A099168 A099169 A099170 * A099172 A099173 A099174

KEYWORD

nonn

AUTHOR

Ralf Stephan, Oct 09 2004

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Last modified February 17 08:44 EST 2012. Contains 205998 sequences.