id:A099171 - OEIS Search Results

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

+0
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; listen)

	OFFSET	`0,2`
	COMMENT	`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 this_sequence A012307 A012311 A012513` `Adjacent sequences: A099168 A099169 A099170 this_sequence A099172 A099173 A099174`
	KEYWORD	`nonn`
	AUTHOR	`Ralf Stephan, Oct 09 2004`

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Last modified December 6 22:55 EST 2009. Contains 170429 sequences.

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