cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A099256 Expansion of g.f. (3-x)*(1+3*x+x^2)/((1-x-x^2)*(1+x-x^2)).

Original entry on oeis.org

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
Offset: 0

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Author

Creighton Dement, Oct 18 2004

Keywords

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

Crossrefs

Cf. A000045, A099255, A000032, A055273 (bisection), A097134 (bisection).

Programs

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

Formula

a(2n+2) - a(2n+1) = Fibonacci(2n-1).
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).

Extensions

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