A022310 a(n) = a(n-1) + a(n-2) + 1 for n>1, a(0)=0, a(1)=5.
0, 5, 6, 12, 19, 32, 52, 85, 138, 224, 363, 588, 952, 1541, 2494, 4036, 6531, 10568, 17100, 27669, 44770, 72440, 117211, 189652, 306864, 496517, 803382, 1299900, 2103283, 3403184, 5506468, 8909653, 14416122, 23325776, 37741899, 61067676, 98809576, 159877253
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,0,-1).
Programs
-
Mathematica
LinearRecurrence[{2, 0, -1}, {0, 5, 6}, 60] (* Vladimir Joseph Stephan Orlovsky, Feb 11 2012 *) -
PARI
concat(0, Vec(x*(5-4*x) / ((1-x)*(1-x-x^2)) + O(x^50))) \\ Colin Barker, Feb 20 2017
Formula
From R. J. Mathar, Apr 07 2011: (Start)
G.f.: -x*(-5 + 4*x)/((x - 1)*(x^2 + x - 1)).
a(n) = A022096(n) - 1. (End)
a(n) = 6*F(n) + F(n-1) - 1, where F = A000045. - Bruno Berselli, Feb 20 2017
From Colin Barker, Feb 20 2017: (Start)
a(n) = -1 + (2^(-1-n)*((1-t)^n*(-11+t) + (1+t)^n*(11+t))) / t where t=sqrt(5).
a(n) = 2*a(n-1) - a(n-3) for n>2. (End)