OFFSET
0,1
COMMENTS
Generalized Fibonacci sequence.
LINKS
FORMULA
G.f.: (2 - 5*x)/(1 - 4*x - 4*x^2).
a(n) = 2^(n-5/2)*((1+4*sqrt(2))*(1-sqrt(2))^n - (1-4*sqrt(2))*(1+sqrt(2))^n).
Lim_{n -> infinity} a(n)/a(n - 1) = 2 + 2*sqrt(2) = 2*A014176 = 4.82842712...
MATHEMATICA
Table[2^(n - 5/2) ((1 + 4 Sqrt[2]) (1 - Sqrt[2])^n - (1 - 4 Sqrt[2]) (1 + Sqrt[2])^n), {n, 0, 25}]
RecurrenceTable[{a[0] == 2, a[1] == 3, a[n] == 4 a[n - 1] + 4 a[n - 2]}, a, {n, 25}] (* Bruno Berselli, Jan 19 2016 *)
LinearRecurrence[{4, 4}, {2, 3}, 20] (* Vincenzo Librandi, Jan 19 2016 *)
PROG
(PARI) Vec((2-5*x)/(1-4*x-4*x^2) + O(x^100)) \\ Altug Alkan, Jan 19 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Jan 19 2016
STATUS
approved