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A006490
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a(1) = 1, a(2) = 0; for n > 2, a(n) = n*Fibonacci(n-2) (with the convention Fibonacci(0)=0, Fibonacci(1)=1).
(Formerly M2362)
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7
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1, 0, 3, 4, 10, 18, 35, 64, 117, 210, 374, 660, 1157, 2016, 3495, 6032, 10370, 17766, 30343, 51680, 87801, 148830, 251758, 425064, 716425, 1205568, 2025675, 3399004, 5696122, 9534330, 15941099, 26625280, 44426877, 74062506, 123360230, 205303932, 341416205, 567353376
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OFFSET
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1,3
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COMMENTS
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Number of circular binary words of length n having exactly one occurrence of 00. Example: a(5)=10 because we have 00111, 10011, 11001, 11100, 01110, 00101, 10010, 01001, 10100 and 01010. Column 1 of A119458. - Emeric Deutsch, May 20 2006
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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MAPLE
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with(combinat): a[1]:=1: a[2]:=0: for n from 3 to 40 do a[n]:=n*fibonacci(n-2) od: seq(a[n], n=1..40); # Emeric Deutsch, May 20 2006
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MATHEMATICA
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Table[Sum[Fibonacci[n - 1], {i, 0, n}], {n, 0, 34}] (* Zerinvary Lajos, Jul 12 2009 *)
CoefficientList[Series[(1 - 2 x + 2 x^2) / (1 - x - x^2)^2, {x, 0, 33}], x] (* or *) LinearRecurrence[{2, 1, -2, -1}, {1, 0, 3, 4}, 40] (* Vincenzo Librandi, Aug 07 2017 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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