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A184959
Fibonacci sequence beginning 10, 9.
0
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
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
Sequence in context: A369603 A309660 A341821 * A309661 A003568 A305196
KEYWORD
nonn,easy
AUTHOR
STATUS
approved