A110935 - OEIS

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

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OFFSET

0,2

COMMENTS

Number of self-avoiding walks on the strip {0,1} X Z.

Variant of A038577. [R. J. Mathar, Dec 13 2008]

LINKS

Table of n, a(n) for n=0..37.

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).

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

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 *)

PROG

(PARI) a(n) = if (n % 2, 8*fibonacci(n)-4, 8*fibonacci(n)-n); \\ Michel Marcus, Sep 07 2015

CROSSREFS

Sequence in context: A119638 A178547 A168674 * A128034 A027150 A020141

Adjacent sequences: A110932 A110933 A110934 * A110936 A110937 A110938

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Sep 30 2007

STATUS

approved