0,1

One of two sequences involving the Lucas/Fibonacci numbers.

This sequence consists of pairs of numbers more or less close to each other with "jumps" in between pairs. "pos((Ex)^n)" sums up over all floretion basis vectors with positive coefficients for each n. The following relations appear to hold: a(2n) - (a(2n-1) + a(2n-2)) = 2*Luc(2n) a(2n+1) - a(2n) = Fib(2n), apart from initial term a(2n+1)/a(2n-1) -> 2 + golden ratio phi a(2n)/a(2n-2) -> 2 + golden ratio phi An identity: (1/2)a(n) - (1/2)A099256(n) = ((-1)^n)A000032(n)

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-1).

a(n) = 2*pos((Ex)^n)

a(0) = 7, a(1) = 6, a(2) = a(3) = 15, a(n+4) = 3a(n+2) - a(n).

a(2n) = A022097(2n+1), a(2n+1) = A022086(2n+3).

a(n) = A061084(n+1)+A013655(n+2). [R. J. Mathar, Nov 30 2008]

LinearRecurrence[{0, 3, 0, -1}, {7, 6, 15, 15}, 40] (* Harvey P. Dale, Dec 29 2012 *)

Cf. A099256, A000032.

Sequence in context: A259168 A309624 A078323 * A198460 A215334 A298377

Adjacent sequences: A099252 A099253 A099254 * A099256 A099257 A099258

nonn,easy

Creighton Dement, Oct 09 2004

More terms from Creighton Dement, Apr 19 2005

approved