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A127210
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a(n) = 3^n*Lucas(n), where Lucas = A000204.
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10
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3, 27, 108, 567, 2673, 13122, 63423, 308367, 1495908, 7263027, 35252253, 171124002, 830642283, 4032042867, 19571909148, 95004113247, 461159522073, 2238515585442, 10865982454983, 52744587633927, 256027604996628, 1242784103695227, 6032600756055333, 29282859201423042
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = Trace of matrix [({3,3},{3,0})^n] = 3^n * Trace of matrix [({1,1},{1,0})^n].
a(n) = 3*a(n-1) + 9*a(n-2).
G.f.: 3*x*(1 + 6*x)/(1 - 3*x - 9*x^2).
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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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PROG
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(PARI) lucas(n) = fibonacci(n-1) + fibonacci(n+1);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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