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A122069
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a(0)=1, a(1)=3, a(n)=3*a(n-1)+9*a(n-2) for n>1.
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1, 3, 18, 81, 405, 1944, 9477, 45927, 223074, 1082565, 5255361, 25509168, 123825753, 601059771, 2917611090, 14162371209, 68745613437, 333698181192, 1619805064509, 7862698824255, 38166342053346, 185263315578333
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n)=3^n*Fibonacci(n+1)=3^n*A000045(n+1) . a(n)=Sum_{k, 0<=k<=n}2^k*A016095(n,k) . G.f.:1/(1-3*x-9*x^2) a(n+1)/a(n)->3*((1+sqrt(5))/2 if n ->infinity.
a(n)=A099012(n+1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 02 2008]
a(n)=(1/2)*[(3/2)+(3/2)*sqrt(5)]^n+(1/10)*[(3/2)+(3/2)*sqrt(5)]^n*sqrt(5)-(1/10)*sqrt(5)*[(3/2)-(3/2) *sqrt(5)]^n+(1/2)*[(3/2)-(3/2)*sqrt(5)]^n, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 19 2008]
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PROG
| (Other) sage: [lucas_number1(n, 3, -9) for n in xrange(1, 23)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
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CROSSREFS
| Sequence in context: A036290 A078904 A099012 * A103897 A119424 A037295
Adjacent sequences: A122066 A122067 A122068 * A122070 A122071 A122072
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KEYWORD
| nonn
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 15 2006
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EXTENSIONS
| Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006
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