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A097136
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a(n) = 3*Fibonacci(2*n) + 1.
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5
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1, 4, 10, 25, 64, 166, 433, 1132, 2962, 7753, 20296, 53134, 139105, 364180, 953434, 2496121, 6534928, 17108662, 44791057, 117264508, 307002466, 803742889, 2104226200, 5508935710, 14422580929, 37758807076, 98853840298, 258802713817, 677554301152
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: (1-2*x^2) / ((1-x)*(1-3*x+x^2)).
a(n) = 4*a(n-1) - 4*a(n-2) + a(n-3).
a(n) = 1+3((3+sqrt(5))/2)^n/sqrt(5)-3((3-sqrt(5))/2)^n/sqrt(5).
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MATHEMATICA
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Table[3*Fibonacci[2n]+1, {n, 0, 30}] (* or *) LinearRecurrence[{4, -4, 1}, {1, 4, 10}, 30] (* Harvey P. Dale, May 25 2018 *)
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PROG
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(PARI) Vec((1-2*x^2)/((1-x)*(1-3*x+x^2)) + O(x^30)) \\ Colin Barker, Nov 02 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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STATUS
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approved
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