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A106517
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Convolution of Fibonacci(n-1) and 3^n.
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4
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1, 3, 10, 31, 95, 288, 869, 2615, 7858, 23595, 70819, 212512, 637625, 1913019, 5739290, 17218247, 51655351, 154967040, 464902717, 1394710735, 4184136386, 12552415923, 37657258715, 112971793856, 338915410225, 1016746277043
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1-x)/((1-x-x^2)*(1-3*x)).
a(n) = Sum_{k=0..n} Fibonacci(n-k-1) * 3^k.
a(n) = (1/5)*(6*3^n - Lucas(n+1)). - Ralf Stephan, Nov 16 2010
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MATHEMATICA
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LinearRecurrence[{4, -2, -3}, {1, 3, 10}, 30] (* Harvey P. Dale, Oct 08 2014 *)
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PROG
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(Magma) I:=[1, 3, 10]; [n le 3 select I[n] else 4*Self(n-1) -2*Self(n-2) -3*Self(n-3): n in [1..41]]; // G. C. Greubel, Aug 05 2021
(Sage) [(2*3^(n+1) - lucas_number2(n+1, 1, -1))/5 for n in (0..40)] # G. C. Greubel, Aug 05 2021
(PARI) a(n) = sum(k=0, n, fibonacci(n-k-1) * 3^k); \\ Michel Marcus, Aug 06 2021
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CROSSREFS
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Diagonal sums of number triangle A106516.
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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