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A271359
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a(n) = k*Fibonacci(2*n+1) + (k+1)*Fibonacci(2*n), where k=5.
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3
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5, 16, 43, 113, 296, 775, 2029, 5312, 13907, 36409, 95320, 249551, 653333, 1710448, 4478011, 11723585, 30692744, 80354647, 210371197, 550758944, 1441905635, 3774957961, 9882968248, 25873946783, 67738872101, 177342669520, 464289136459, 1215524739857
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: (5+x) / (1-3*x+x^2).
a(n) = 3*a(n-1)-a(n-2) for n>1.
a(n) = (2^(-2-n)*((13-sqrt(5))*(3+sqrt(5))^(n+1) - (13+sqrt(5))*(3-sqrt(5))^(n+1))) / sqrt(5).
a(n) = 6*Fibonacci(2*n+2) - Fibonacci(2*n+1) = 5*A001906(n+1) +A001906(n).
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PROG
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(PARI) a(n) = 5*fibonacci(2*n+1) + 6*fibonacci(2*n)
(PARI) Vec((5+x)/(1-3*x+x^2) + O(x^50))
(Magma) k:=5; [k*Fibonacci(2*n+1)+(k+1)*Fibonacci(2*n): n in [0..30]]; // Bruno Berselli, Apr 06 2016
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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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Changed offset and adapted definition, programs and formulas by Bruno Berselli, Apr 06 2016
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STATUS
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approved
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