

A099256


G.f.: (3x)(1+3x+x^2)/((1xx^2)(1+xx^2)).


2



3, 8, 9, 23, 24, 61, 63, 160, 165, 419, 432, 1097, 1131, 2872, 2961, 7519, 7752, 19685, 20295, 51536, 53133, 134923, 139104, 353233, 364179, 924776, 953433, 2421095, 2496120, 6338509, 6534927, 16594432, 17108661, 43444787, 44791056, 113739929, 117264507, 297775000, 307002465, 779585071
(list;
graph;
refs;
listen;
history;
text;
internal format)



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.
a(n+3) + a(n)  a(n+2) appears to be mysteriously connected with a(n+1).
Both this sequence and A099255 were created using "Floretion dynamical symmetries" (see link for further details).


LINKS

Table of n, a(n) for n=0..39.
Index entries for linear recurrences with constant coefficients, signature (0,3,0,1).


FORMULA

a(2n+2)  a(2n+1) = F(2n1).
A099255(n)/2  a(n)/2 = (1)^n*A000032(n)
a(0) = 3, a(1) = 8, a(2) = 9, a(3) = 23, a(n+4) = 3a(n+2)  a(n).
a(2n) = A022086(2n+2), a(2n+1) = A022097(2n+2).
a(n) = A013655(n+2)A061084(n+1).


MATHEMATICA

LinearRecurrence[{0, 3, 0, 1}, {3, 8, 9, 23}, 40] (* Harvey P. Dale, Apr 22 2012 *)


PROG

Floretion Algebra Multiplication Program, FAMP


CROSSREFS

Cf. A099255, A000032, A055273 (bisection), A097134 (bisection).
Sequence in context: A212849 A191487 A176205 * A167344 A025615 A297324
Adjacent sequences: A099253 A099254 A099255 * A099257 A099258 A099259


KEYWORD

nonn,easy


AUTHOR

Creighton Dement, Oct 18 2004


EXTENSIONS

Definition corrected, extended.  R. J. Mathar, Nov 13 2008


STATUS

approved



