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Search: id:A117641
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| A117641 |
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Number of 3-Motzkin paths with no level steps at height 0. |
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+0
10
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| 1, 0, 1, 3, 11, 42, 167, 684, 2867, 12240, 53043, 232731, 1031829, 4615542, 20805081, 94410363, 430945739, 1977366192, 9115261211, 42195093993, 196060049129, 914110333422, 4275222950221, 20051858039718, 94294269673861
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Hankel transform of this sequence forms A000012 = [1,1,1,1,1,...] . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 24 2007
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FORMULA
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Generating function = (1+3z-sqrt(1-6z+5z^2))/(2z^2+6z).
G.f. as continued fraction is 1/(1-0*x-x^2/(1-3*x-x^2/(1-3*x-x^2/(1-3*x-x^2/(..... [From Paul Barry (pbarry(AT)wit.ie), Dec 02 2008]
a(n)= A126970(n,0). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 24 2009]
a(n)= Sum_{k, 0<=k<=n} A091965(n,k)*(-3)^k. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 28 2009]
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EXAMPLE
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The a(4) = 11 paths are UUDD, UDUD and 9 of the form UXYD where each of X and Y are level steps in any of three colors.
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MATHEMATICA
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CoefficientList[ Series[(1 + 3x - Sqrt[1 - 6x + 5x^2])/(2x^2 + 6x), {x, 0, 25}], x] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A000957, A001006, A002212, A005043, A097331, A000108.
Sequence in context: A122368 A032443 A143464 this_sequence A084782 A149068 A151088
Adjacent sequences: A117638 A117639 A117640 this_sequence A117642 A117643 A117644
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KEYWORD
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easy,nonn,new
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AUTHOR
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Louis Shapiro (lshapiro(AT)howard.edu), Apr 10 2006
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Apr 12 2006
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