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A035508
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Fibonacci(2n+2)-1.
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3
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0, 2, 7, 20, 54, 143, 376, 986, 2583, 6764, 17710, 46367, 121392, 317810, 832039, 2178308, 5702886, 14930351, 39088168, 102334154, 267914295, 701408732, 1836311902, 4807526975, 12586269024, 32951280098, 86267571271, 225851433716
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| C. Kimberling, "Interspersions and dispersions," Proceedings of the American Mathematical Society 117 (1993) 313-321.
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LINKS
| Guo-Niu Han, Enumeration of Standard Puzzles
C. Kimberling, Interspersions
N. J. A. Sloane, Classic Sequences
Index to sequences with linear recurrences with constant coefficients, signature (4,-4,1).
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FORMULA
| G.f.: x(2-x)/((1-x)(1-3x+x^2)). a(n)=4*a(n-1)-4*a(n-2)+a(n-3). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 15 2008]
a(n)= Fibonacci(4n+2) mod Fibonacci(2n+2) [From Gary Detlefs (gdetlefs(AT)aol.com) Nov 22 2010]
a(n+1)= sum(Fibonacci(2*k+3), k=0..n)) [From Gary Detlefs (gdetlefs(AT)aol.com) Dec 24 2010]
a(n) = sum_{i=1..n} A112844(i). - R. J. Mathar, Apr 19 2011
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MAPLE
| (Mupad) numlib::fibonacci(2*n)-1 $ n = 1..38; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 08 2008
g:=z/(1-3*z+z^2): gser:=series(g, z=0, 43): seq(abs(coeff(gser, z, n)-1), n=1..26); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 22 2009]
with(combinat):seq(fibonacci(4*n+2) mod fibonacci(2*n+2), n=0..25);
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MATHEMATICA
| Fibonacci[2*Range[0, 5!]]-1 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), May 18 2010]
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PROG
| (Other) sage: [lucas_number1(n, 3, 1)-1 for n in xrange(1, 27)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 07 2009]
(MAGMA) [Fibonacci(2*n+2)-1: n in [0..30]]; // Vincenzo Librandi, Apr 18 2011
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CROSSREFS
| a(n)=A001906(n)-1.
With different offset: 2nd row of Inverse Stolarsky array A035507.
Cf. A152891 (partial sums).
Sequence in context: A050513 A128183 A027418 * A018033 A000149 A080041
Adjacent sequences: A035505 A035506 A035507 * A035509 A035510 A035511
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| G.f. adapted to the offset by Bruno Berselli, Apr 19 2011
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