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A127210
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3^n*Lucas(n), with A000204 the Lucas numbers.
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9
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3, 27, 108, 567, 2673, 13122, 63423, 308367, 1495908, 7263027, 35252253, 171124002, 830642283, 4032042867, 19571909148, 95004113247, 461159522073, 2238515585442, 10865982454983, 52744587633927
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..20.
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FORMULA
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a(n) = Trace of matrix [({3,3},{3,0})^n] a(n) = 3^n Trace of matrix [({1,1},{1,0})^n]
a(n)= 3*a(n-1)+9*a(n-2). G.f.: 3x(1+6x)/(1-3x-9x^2). a(n) = 3*A099012(n) +18*A099012(n-1). [From R. J. Mathar, Oct 27 2008]
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MATHEMATICA
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Table[3^n Tr[MatrixPower[{{1, 1}, {1, 0}}, x]], {x, 1, 20}]
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CROSSREFS
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Cf. A087131, A127211, A127212, A127213, A127214, A127215, A127216.
Sequence in context: A200977 A173491 A195799 * A161807 A063263 A204809
Adjacent sequences: A127207 A127208 A127209 * A127211 A127212 A127213
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski, Jan 09 2007
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STATUS
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approved
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