login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A099256 G.f.: (3-x)(1+3x+x^2)/((1-x-x^2)(1+x-x^2)). 2

%I

%S 3,8,9,23,24,61,63,160,165,419,432,1097,1131,2872,2961,7519,7752,

%T 19685,20295,51536,53133,134923,139104,353233,364179,924776,953433,

%U 2421095,2496120,6338509,6534927,16594432,17108661,43444787,44791056,113739929,117264507,297775000,307002465,779585071

%N G.f.: (3-x)(1+3x+x^2)/((1-x-x^2)(1+x-x^2)).

%C 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.

%C a(n+3) + a(n) - a(n+2) appears to be mysteriously connected with a(n+1).

%C Both this sequence and A099255 were created using "Floretion dynamical symmetries" (see link for further details).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-1).

%F a(2n+2) - a(2n+1) = F(2n-1).

%F A099255(n)/2 - a(n)/2 = (-1)^n*A000032(n)

%F a(0) = 3, a(1) = 8, a(2) = 9, a(3) = 23, a(n+4) = 3a(n+2) - a(n).

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

%F a(n) = A013655(n+2)-A061084(n+1).

%t LinearRecurrence[{0,3,0,-1},{3,8,9,23},40] (* _Harvey P. Dale_, Apr 22 2012 *)

%o Floretion Algebra Multiplication Program, FAMP

%Y Cf. A099255, A000032, A055273 (bisection), A097134 (bisection).

%K nonn,easy

%O 0,1

%A _Creighton Dement_, Oct 18 2004

%E Definition corrected, extended. - _R. J. Mathar_, Nov 13 2008

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 11 21:15 EST 2017. Contains 295919 sequences.