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A110935
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a(n) = if n mod 2 = 0 then 8*F(n)-n otherwise 8*F(n)-4, where F() = Fibonacci numbers A000045.
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1
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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
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0,2
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COMMENTS
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Number of self-avoiding walks on the strip {0,1} X Z.
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n) = if (n % 2, 8*fibonacci(n)-4, 8*fibonacci(n)-n); \\ Michel Marcus, Sep 07 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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