id:A132900 - OEIS Search Results

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Coloured Motzkin paths where each of the steps has three possible colours.

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1, 3, 18, 108, 729, 5103, 37179, 277749, 2119203, 16435305, 129199212, 1027098306, 8243181351, 66698502705, 543507899346, 4456368744804, 36738955831707, 304354824214977, 2532328310730798, 21152326520189628 (list; graph; listen)

	OFFSET	`0,2`
	COMMENT	`Reversion of x/(1+3x+9x^2).`
	FORMULA	`G.f.: (1-3x-sqrt(1-6x-27x^2))/(18x^2); a(n)=3^nA001006(n)=sum{k=0..floor(n/2), C(n,2k)C(k)3^(n-2k)3^k3^k} where C(n)=A000108(n); a(n)=(1/(2pi))int(x^n*sqrt(27+6x-x^2)/9,x,-3,9);`
	CROSSREFS	`Cf. A129400.` `Sequence in context: A025595 A137962 A081341 this_sequence A050623 A037760 A037648` `Adjacent sequences: A132897 A132898 A132899 this_sequence A132901 A132902 A132903`
	KEYWORD	`easy,nonn`
	AUTHOR	`Paul Barry (pbarry(AT)wit.ie), Sep 04 2007`

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Last modified July 26 13:41 EDT 2008. Contains 142293 sequences.

AT&T Labs Research