A187890 a(1) = 0, a(2) = 4, a(n) = a(n-1) + a(n-2) - 1.
0, 4, 3, 6, 8, 13, 20, 32, 51, 82, 132, 213, 344, 556, 899, 1454, 2352, 3805, 6156, 9960, 16115, 26074, 42188, 68261, 110448, 178708, 289155, 467862, 757016, 1224877, 1981892, 3206768, 5188659, 8395426, 13584084, 21979509, 35563592, 57543100
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (2,0,-1).
Programs
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Mathematica
Join[{a = 0, b = 4}, Table[c = a+b-1; a=b; b=c, {n, 100}]] LinearRecurrence[{2, 0, -1}, {0, 4, 3}, 40] (* Harvey P. Dale, Sep 25 2013 *) CoefficientList[Series[(-x (-4 + 5 x))/((x - 1) (x^2 + x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 26 2013 *)
Formula
G.f.: -x^2*(-4+5*x) / ( (x-1)*(x^2+x-1) ). - R. J. Mathar, Mar 15 2011
a(n) = 1+A001060(n-2), n>2. - R. J. Mathar, Mar 15 2011
a(n) - a(n-1) = A013655(n-4). - R. J. Mathar, Jun 19 2021
If we start the sequence 1, 3, 6, ... and set the offset to 0, then the sequence has the generating function (1 + x - 3*x^3)/(x^3 - 2*x + 1) and gives the row sums of A374438. - Peter Luschny, Jul 22 2024
Extensions
Definition adapted to offset by Georg Fischer, Jun 19 2021