A184959 Fibonacci sequence beginning 10, 9.

10, 9, 19, 28, 47, 75, 122, 197, 319, 516, 835, 1351, 2186, 3537, 5723, 9260, 14983, 24243, 39226, 63469, 102695, 166164, 268859, 435023, 703882, 1138905, 1842787, 2981692, 4824479, 7806171, 12630650, 20436821, 33067471, 53504292, 86571763, 140076055

Offset

0,1

Links

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (1,1).

Formula

From Benedict W. J. Irwin, May 30 2016: (Start)

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

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

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

(End)

a(n) = Lucas(n+4) - Fibonacci(n-4). - Greg Dresden and Erin Addison, Mar 02 2022

Mathematica

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

Crossrefs

Cf. A000032, A000045.

Sequence in context: A369603 A309660 A341821 * A309661 A003568 A305196

Adjacent sequences: A184956 A184957 A184958 * A184960 A184961 A184962

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Feb 28 2011

Status

approved