A110935 a(n) = if n mod 2 = 0 then 8*F(n)-n otherwise 8*F(n)-4, where F() = Fibonacci numbers A000045.
0, 4, 6, 12, 20, 36, 58, 100, 160, 268, 430, 708, 1140, 1860, 3002, 4876, 7880, 12772, 20654, 33444, 54100, 87564, 141666, 229252, 370920, 600196, 971118, 1571340, 2542460, 4113828, 6656290, 10770148, 17426440, 28196620, 45623062, 73819716, 119442780, 193262532
Offset: 0
Links
- A. T. Benjamin, Self-avoiding walks and Fibonacci numbers, Fib. Quart., 44 (No. 4, 2006), 330-334.
- Doron Zeilberger, Self Avoiding Walks, The Language of Science, and Fibonacci Numbers, arXiv:math/9506214 [math.CO], Jun 03 1995.
- Index entries for linear recurrences with constant coefficients, signature (1,3,-2,-3,1,1).
Programs
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Mathematica
LinearRecurrence[{1, 3, -2, -3, 1, 1}, {0, 4, 6, 12, 20, 36}, 40] (* Jean-François Alcover, Jan 09 2019 *) Table[If[EvenQ[n],8Fibonacci[n]-n,8Fibonacci[n]-4],{n,0,40}] (* Harvey P. Dale, Jun 12 2019 *) -
PARI
a(n) = if (n % 2, 8*fibonacci(n)-4, 8*fibonacci(n)-n); \\ Michel Marcus, Sep 07 2015
Formula
G.f.: -2*x*(2*x^4-x^3-3*x^2+x+2) / ((x-1)^2*(x+1)^2*(x^2+x-1)). - Colin Barker, Mar 18 2013
Comments