

A099255


G.f. (7+6*x6*x^23*x^3)/((x^2+x1)*(x^2x1)).


2



7, 6, 15, 15, 38, 39, 99, 102, 259, 267, 678, 699, 1775, 1830, 4647, 4791, 12166, 12543, 31851, 32838, 83387, 85971, 218310, 225075, 571543, 589254, 1496319, 1542687, 3917414, 4038807, 10255923, 10573734, 26850355, 27682395, 70295142, 72473451
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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(2n1) + a(2n2)) = 2*Luc(2n) a(2n+1)  a(2n) = Fib(2n), apart from initial term a(2n+1)/a(2n1) > 2 + golden ratio phi a(2n)/a(2n2) > 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).
a(2n) = A022097(2n+1), a(2n+1) = A022086(2n+3).
a(n)=A061084(n+1)+A013655(n+2). [From R. J. Mathar, Nov 30 2008]


MATHEMATICA

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


PROG

Floretion Algebra Multiplication Program, FAMP


CROSSREFS

Cf. A099256, A000032.
Sequence in context: A297153 A259168 A078323 * A198460 A215334 A298377
Adjacent sequences: A099252 A099253 A099254 * A099256 A099257 A099258


KEYWORD

nonn,easy


AUTHOR

Creighton Dement, Oct 09 2004


EXTENSIONS

More terms from Creighton Dement, Apr 19 2005


STATUS

approved



