A184959 - OEIS

%I #49 Oct 17 2024 08:28:19

%S 10,9,19,28,47,75,122,197,319,516,835,1351,2186,3537,5723,9260,14983,

%T 24243,39226,63469,102695,166164,268859,435023,703882,1138905,1842787,

%U 2981692,4824479,7806171,12630650,20436821,33067471,53504292,86571763,140076055

%N Fibonacci sequence beginning 10, 9.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).

%F From _Benedict W. J. Irwin_, May 30 2016: (Start)

%F G.f.: (z-10)/(z^2+z-1).

%F E.g.f: (2*exp(z/2)/5)*(25*cosh(sqrt(5)*z/2)+4*sqrt(5)*sinh(sqrt(5)*z/2)).

%F a(n) = (2^(-n)/sqrt(5))*((1-sqrt(5))^n*(5*sqrt(5)-4)+(1+sqrt(5))^n*(5*sqrt(5)+4)).

%F (End)

%F a(n) = Lucas(n+4) - Fibonacci(n-4). - _Greg Dresden_ and Erin Addison, Mar 02 2022

%t LinearRecurrence[{1, 1}, {10, 9}, 100]

%Y Cf. A000032, A000045.

%K nonn,easy

%O 0,1

%A _Vladimir Joseph Stephan Orlovsky_, Feb 28 2011