OFFSET
0,1
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,2).
FORMULA
a(n) = trace(M^n) where M is [1, 2; 3, 4].
From Colin Barker, Sep 27 2019: (Start)
G.f.: (2 - 5*x) / (1 - 5*x - 2*x^2).
a(n) = 5*a(n-1) + 2*a(n-2) for n > 1.
a(n) = ((5-sqrt(33))/2)^n + ((5+sqrt(33))/2)^n.
(End)
MAPLE
a:= n-> (<<0|1>, <2|5>>^n. <<2, 5>>)[1, 1]:
seq(a(n), n=0..23); # Alois P. Heinz, Oct 07 2019
MATHEMATICA
CoefficientList[Series[(2 - 5 x)/(1 - 5 x - 2 x^2), {x, 0, 22}], x] (* Michael De Vlieger, Sep 27 2019 *)
LinearRecurrence[{5, 2}, {2, 5}, 30] (* Harvey P. Dale, Jun 25 2020 *)
PROG
(PARI) a(n)={trace([1, 2; 3, 4]^n)} \\ Andrew Howroyd, Sep 24 2019
(PARI) Vec((2 - 5*x) / (1 - 5*x - 2*x^2) + O(x^25)) \\ Colin Barker, Sep 27 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Adolf Cusmariu, Sep 24 2019
STATUS
approved