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A022319
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a(n) = a(n-1) + a(n-2) + 1 for n > 1, a(0)=1, a(1)=5.
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6
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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
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OFFSET
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0,2
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,-1).
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FORMULA
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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)
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MAPLE
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with(combinat): seq(fibonacci(n-2)+fibonacci(n+4)-1, n=0..29); # Zerinvary Lajos, Feb 01 2008
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MATHEMATICA
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LinearRecurrence[{2, 0, -1}, {1, 5, 7}, 40] (* Harvey P. Dale, Nov 19 2014 *)
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PROG
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(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
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CROSSREFS
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Cf. A192762 (partial sums).
Sequence in context: A154872 A314330 A349576 * A207079 A167798 A165815
Adjacent sequences: A022316 A022317 A022318 * A022320 A022321 A022322
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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