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A033192
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a(n) = binomial(Fibonacci(n) + 1, 2).
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9
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0, 1, 1, 3, 6, 15, 36, 91, 231, 595, 1540, 4005, 10440, 27261, 71253, 186355, 487578, 1276003, 3339820, 8742471, 22885995, 59912931, 156848616, 410626153, 1075018896, 2814412825, 7368190921, 19290113571, 50502074766, 132215989335, 346145696820, 906220783315
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OFFSET
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0,4
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COMMENTS
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LINKS
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FORMULA
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G.f.: x(x^3-x^2-2x+1)/[(1+x)(1-3x+x^2)(1-x-x^2)].
a(n) = ((Fibonacci(n)+Fibonacci(n)^2)/2). - Gary Detlefs, Dec 24 2010
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MAPLE
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a:= n-> (f-> f*(f+1)/2)((<<0|1>, <1|1>>^n)[1, 2]):
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MATHEMATICA
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Table[Binomial[Fibonacci[n] + 1, 2], {n, 0, 50}] (* Alonso del Arte, Jan 26 2012 *)
LinearRecurrence[{3, 1, -5, -1, 1}, {0, 1, 1, 3, 6}, 40] (* Harvey P. Dale, Apr 04 2020 *)
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PROG
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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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Simon P. Norton
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STATUS
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approved
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