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A035508
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a(n) = Fibonacci(2n+2) - 1.
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4
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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
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refs;
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history;
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..27.
Guo-Niu Han, Enumeration of Standard Puzzles
Guo-Niu Han, Enumeration of Standard Puzzles [Cached copy]
C. Kimberling, Interspersions
C. Kimberling, Interspersions and dispersions, Proceedings of the American Mathematical Society, 117 (1993) 313-321.
N. J. A. Sloane, Classic Sequences
Index entries for linear recurrences with constant coefficients, signature (4,-4,1).
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FORMULA
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a(n) = A001906(n) - 1.
G.f.: x(2-x)/((1-x)(1 - 3x + x^2)). a(n) = 4*a(n-1) - 4*a(n-2) + a(n-3). - R. J. Mathar, Dec 15 2008
a(n) = Fibonacci(4n+2) mod Fibonacci(2n+2). - Gary Detlefs Nov 22 2010
a(n+1) = sum_{k=0..n} Fibonacci(2*k+3). - Gary Detlefs Dec 24 2010
a(n) = sum_{i=1..n} A112844(i). - R. J. Mathar, Apr 19 2011
a(n) = floor(Fibonacci(2*n+2)- Fibonacci(n+1)^2/Fibonacci(2*n+2)). - Gary Detlefs, Dec 21 2012
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MAPLE
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(MuPAD) numlib::fibonacci(2*n)-1 $ n = 1..38; // Zerinvary Lajos, 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); # Zerinvary Lajos, Mar 22 2009
with(combinat):seq(fibonacci(4*n+2) mod fibonacci(2*n+2), n=0..25);
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MATHEMATICA
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Fibonacci[2*Range[0, 5!]] - 1 (* Vladimir Joseph Stephan Orlovsky, May 18 2010 *)
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PROG
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(Sage) [lucas_number1(n, 3, 1)-1 for n in xrange(1, 27)] # Zerinvary Lajos, Dec 07 2009
(MAGMA) [Fibonacci(2*n+2)-1: n in [0..30]]; // Vincenzo Librandi, Apr 18 2011
(Maxima) makelist(fib(2*n+2)-1, n, 0, 30); /* Martin Ettl, Oct 21 2012 */
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CROSSREFS
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With different offset: 2nd row of Inverse Stolarsky array A035507.
Cf. A001906, 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
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nonn
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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G.f. adapted to the offset by Bruno Berselli, Apr 19 2011
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STATUS
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approved
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