OFFSET
0,2
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-4,1).
FORMULA
a(n) = Fibonacci(2*n+3) + 2*Fibonacci(2*n+2) - 3.
From Colin Barker, Feb 18 2016: (Start)
a(n) = 2^(-n)*(-3*2^n-(3-sqrt(5))^n*(-2+sqrt(5))+(2+sqrt(5))*(3+sqrt(5))^n).
a(n) = 4*a(n-1)-4*a(n-2)+a(n-3) for n>2.
G.f.: (1+4*x-2*x^2) / ((1-x)*(1-3*x+x^2)).
(End)
PROG
(Magma) [Fibonacci(2*n+3) + 2*Fibonacci(2*n+2) - 3: n in [0..30]]; // Vincenzo Librandi, Apr 18 2011
(PARI) Vec((1+4*x-2*x^2)/((1-x)*(1-3*x+x^2)) + O(x^40)) \\ Colin Barker, Feb 18 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved