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A035508 a(n) = Fibonacci(2n+2) - 1. 4
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; text; internal format)
OFFSET

0,2

LINKS

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).

FORMULA

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

MAPLE

(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);

MATHEMATICA

Fibonacci[2*Range[0, 5!]] - 1 (* Vladimir Joseph Stephan Orlovsky, May 18 2010 *)

PROG

(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 */

CROSSREFS

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

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

G.f. adapted to the offset by Bruno Berselli, Apr 19 2011

STATUS

approved

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Last modified February 24 06:13 EST 2018. Contains 299597 sequences. (Running on oeis4.)