OFFSET
1,1
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (4,-4,-1,2).
FORMULA
a(n) = 4*a(n-1) -4*a(n-2) -a(n-3) +2*a(n-4). G.f.: x*(2-4*x+x^2)/((x-1) * (2*x-1) * (1-x-x^2)). - R. J. Mathar, Feb 06 2010
a(n) = ((1+sqrt(5))^n-(1-sqrt(5))^n)/(2^n*sqrt(5)) + 2^n - 1. - Colin Barker, Nov 02 2016
MAPLE
seq(2^x-1+fibonacci(x), x=1..30);
MATHEMATICA
Table[2^n-1+Fibonacci[n], {n, 30}] (* or *) LinearRecurrence[{4, -4, -1, 2}, {2, 4, 9, 18}, 30] (* Harvey P. Dale, Aug 24 2012 *)
PROG
(Sage) [gaussian_binomial(n, 1, 2)+fibonacci (n) for n in range(1, 31)] # Zerinvary Lajos, May 29 2009
(PARI) Vec(x*(2-4*x+x^2)/((1-x)*(1-2*x)*(1-x-x^2)) + O(x^30)) \\ Colin Barker, Nov 02 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jorge Coveiro, Dec 25 2004
EXTENSIONS
Offset changed to 1 by Colin Barker, Nov 02 2016
STATUS
approved