OFFSET
0,1
COMMENTS
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)
LINKS
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).
FORMULA
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).
MATHEMATICA
LinearRecurrence[{0, 3, 0, -1}, {7, 6, 15, 15}, 40] (* Harvey P. Dale, Dec 29 2012 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Creighton Dement, Oct 09 2004
EXTENSIONS
More terms from Creighton Dement, Apr 19 2005
STATUS
approved