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.
%I A110935 #25 Jan 05 2025 19:51:38
%S A110935 0,4,6,12,20,36,58,100,160,268,430,708,1140,1860,3002,4876,7880,12772,
%T A110935 20654,33444,54100,87564,141666,229252,370920,600196,971118,1571340,
%U A110935 2542460,4113828,6656290,10770148,17426440,28196620,45623062,73819716,119442780,193262532
%N A110935 a(n) = if n mod 2 = 0 then 8*F(n)-n otherwise 8*F(n)-4, where F() = Fibonacci numbers A000045.
%C A110935 Number of self-avoiding walks on the strip {0,1} X Z.
%C A110935 Variant of A038577. [_R. J. Mathar_, Dec 13 2008]
%H A110935 A. T. Benjamin, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/44-4/quartbenjamin04_2006.pdf">Self-avoiding walks and Fibonacci numbers</a>, Fib. Quart., 44 (No. 4, 2006), 330-334.
%H A110935 Doron Zeilberger, <a href="http://arxiv.org/abs/math/9506214">Self Avoiding Walks, The Language of Science, and Fibonacci Numbers</a>, arXiv:math/9506214 [math.CO], Jun 03 1995.
%H A110935 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-2,-3,1,1).
%F A110935 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
%t A110935 LinearRecurrence[{1, 3, -2, -3, 1, 1}, {0, 4, 6, 12, 20, 36}, 40] (* _Jean-François Alcover_, Jan 09 2019 *)
%t A110935 Table[If[EvenQ[n],8Fibonacci[n]-n,8Fibonacci[n]-4],{n,0,40}] (* _Harvey P. Dale_, Jun 12 2019 *)
%o A110935 (PARI) a(n) = if (n % 2, 8*fibonacci(n)-4, 8*fibonacci(n)-n); \\ _Michel Marcus_, Sep 07 2015
%K A110935 nonn,easy
%O A110935 0,2
%A A110935 _N. J. A. Sloane_, Sep 30 2007