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A132900
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Coloured Motzkin paths where each of the steps has three possible colors.
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0
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Reversion of x/(1+3x+9x^2).
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FORMULA
| G.f.: (1-3x-sqrt(1-6x-27x^2))/(18x^2); a(n)=3^n*A001006(n)=sum{k=0..floor(n/2), C(n,2k)*C(k)3^(n-2k)*3^k*3^k} where C(n)=A000108(n); a(n)=(1/(2*pi))*int(x^n*sqrt(27+6x-x^2)/9,x,-3,9);
Conjecture: (n+2)*a(n) -3*(2*n+1)*a(n-1) +27*(1-n)*a(n-2)=0. - R. J. Mathar, Nov 14 2011
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CROSSREFS
| Cf. A129400.
Sequence in context: A137962 A169604 A081341 * A050623 A037760 A037648
Adjacent sequences: A132897 A132898 A132899 * A132901 A132902 A132903
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 04 2007
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