OFFSET
0,1
LINKS
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (1,1).
FORMULA
From Alois P. Heinz, Jul 31 2008: (Start)
G.f.: (4+9*x)/(1-x-x^2).
a(n) = term (1,1) in the 1x2 matrix [4,9] . [1,1; 1,0]^n. (End)
a(n) = Lucas(n+4) + Fibonacci(n-4). - Greg Dresden and Kyle Wood, Mar 03 2022
MAPLE
a:= n -> (Matrix([[4, 9]]).Matrix([[1, 1], [1, 0]])^n)[1, 1]:
seq(a(n), n=0..35); # Alois P. Heinz, Jul 31 2008
MATHEMATICA
LinearRecurrence[{1, 1}, {4, 13}, 40] (* Harvey P. Dale, Jul 04 2017 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved