A022315 - OEIS

%I #19 Aug 25 2017 23:37:14

%S 0,10,11,22,34,57,92,150,243,394,638,1033,1672,2706,4379,7086,11466,

%T 18553,30020,48574,78595,127170,205766,332937,538704,871642,1410347,

%U 2281990,3692338,5974329,9666668

%N a(n) = a(n-1) + a(n-2) + 1, with a(0) = 0 and a(1) = 10.

%H G. C. Greubel, <a href="/A022315/b022315.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1).

%F From _R. J. Mathar_, Apr 07 2011: (Start)

%F G.f.: x*(10-9*x)/( (1-x)*(1-x-x^2) ).

%F a(n) = A022101(n) - 1. (End)

%F a(n) = F(n+2) + 9*F(n) - 1, where F = A000045. - _G. C. Greubel_, Aug 25 2017

%t CoefficientList[Series[(10 x-9 x^2)/(1-2 x+x^3),{x,0,30}],x]  (* _Harvey P. Dale_, Mar 05 2011 *)

%o (PARI) x='x+O('x^50); concat([0], Vec(x*(10-9*x)/( (1-x)*(1-x-x^2) ))) \\ _G. C. Greubel_, Aug 25 2017

%K nonn

%O 0,2

%A _N. J. A. Sloane_