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Search: id:A006490
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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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+0
4
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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
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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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 (deutsch(AT)duke.poly.edu), 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).
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
L. Carlitz and R. Scoville, Zero-one sequences and Fibonacci numbers, Fib. Quart., 15 (1977), 246-254.
J. P. McSorley, Counting structures in the Moebius ladder, Discrete Math., 184 (1998), 137-164.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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G.f.=x(1-2x+2x^2)/(1-x-x^2)^2. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 20 2006
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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 (deutsch(AT)duke.poly.edu), May 20 2006
A006490:=(1-2*z+2*z**2)/(z**2+z-1)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
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Table[Sum[Fibonacci[n - 1], {i, 0, n}], {n, 0, 34}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 12 2009]
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CROSSREFS
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Cf. A119458.
Sequence in context: A034774 A144958 A034775 this_sequence A139797 A036649 A109887
Adjacent sequences: A006487 A006488 A006489 this_sequence A006491 A006492 A006493
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Better definition from Ralf Stephan, Nov 18 2004
More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 20 2006
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