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A022319 a(n) = a(n-1) + a(n-2) + 1 for n > 1, a(0)=1, a(1)=5. 6
1, 5, 7, 13, 21, 35, 57, 93, 151, 245, 397, 643, 1041, 1685, 2727, 4413, 7141, 11555, 18697, 30253, 48951, 79205, 128157, 207363, 335521, 542885, 878407, 1421293, 2299701, 3720995, 6020697, 9741693 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,-1).

FORMULA

a(n) = Fibonacci(n-2) + Fibonacci(n+4) - 1. - Zerinvary Lajos, Feb 01 2008

From R. J. Mathar, Apr 07 2011: (Start)

G.f.: (1 + 3*x - 3*x^2) / ((1-x)*(1 - x - x^2)).

a(n) = A022112(n) - 1. (End)

MAPLE

with(combinat): seq(fibonacci(n-2)+fibonacci(n+4)-1, n=0..29); # Zerinvary Lajos, Feb 01 2008

MATHEMATICA

LinearRecurrence[{2, 0, -1}, {1, 5, 7}, 40] (* Harvey P. Dale, Nov 19 2014 *)

PROG

(Haskell)

a022319 n = a022319_list !! (n-1)

a022319_list = 1 : 5 : zipWith (+)

   (map (+ 1) a022319_list) (tail a022319_list)

-- Reinhard Zumkeller, May 26 2013

(PARI) x='x+O('x^50); Vec((1 +3*x -3*x^2)/((1-x)*(1 -x -x^2))) \\ G. C. Greubel, Aug 25 2017

CROSSREFS

Cf. A192762 (partial sums).

Sequence in context: A154872 A314330 A349576 * A207079 A167798 A165815

Adjacent sequences:  A022316 A022317 A022318 * A022320 A022321 A022322

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 27 07:25 EDT 2022. Contains 354093 sequences. (Running on oeis4.)