|
| |
|
|
A006490
|
|
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)
|
|
4
| |
|
|
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; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| 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
|
|
|
REFERENCES
| 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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| 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.
|
|
|
FORMULA
| G.f.=x(1-2x+2x^2)/(1-x-x^2)^2. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 20 2006
|
|
|
MAPLE
| 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.]
|
|
|
MATHEMATICA
| Table[Sum[Fibonacci[n - 1], {i, 0, n}], {n, 0, 34}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 12 2009]
|
|
|
CROSSREFS
| Cf. A119458.
Sequence in context: A172416 A144958 A034775 * A171160 A139797 A036649
Adjacent sequences: A006487 A006488 A006489 * A006491 A006492 A006493
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| Better definition from Ralf Stephan, Nov 18 2004
More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 20 2006
|
| |
|
|
