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A110935 a(n) = if n mod 2 = 0 then 8*F(n)-n otherwise 8*F(n)-4, where F() = Fibonacci numbers A000045. 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified January 21 03:58 EST 2022. Contains 350473 sequences. (Running on oeis4.)