|
%I #27 Jan 12 2023 18:49:59
%S 9977,10081,10185,10289,10393,10497,10601,10705,10809,10913,11017,
%T 11121,11225,11329,11433,11537,11641,11745,11849,11953,12057,12161,
%U 12265,12369,12473,12577,12681,12785,12889,12993,13097,13201,13305,13409,13513,13617
%N a(n) = 104*n + 9977.
%C Langton's Ant Superhighway, the start point (9977th iteration, J. Propp) and the period length for the Superhighway (104).
%H B. D. Swan, <a href="/A126978/b126978.txt">Table of n, a(n) for n = 0..10000</a>
%H C. Langton, <a href="http://dx.doi.org/10.1016/0167-2789(86)90237-X">Studying Artificial Life with Cellular Automata</a>, Physica D: Nonlinear Phenomena, vol. 22, pp. 120-149, 1986.
%H Ed Pegg Jr, <a href="http://www.maa.org/editorial/mathgames/mathgames_06_07_04.html">2D Turing Machines </a>.
%H James Propp, <a href="http://dx.doi.org/10.1007/BF03026614">Further Ant-ics</a>, Mathematical Intelligencer, 16 pp. 37-42, 1994.
%H P. Sarkar, <a href="https://www.cs.ucf.edu/~dcm/Teaching/COT4810-Spring2011/Literature/CellularAutomata.pdf">A Brief History of Cellular Automata</a>, ACM Computing Surveys. Vol. 32 No. Mar 01 2000.
%H S. Wolfram, <a href="https://www.wolframscience.com/nks/p185--turing-machines/">2D Turing Machines</a>.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1).
%F a(0)=9977, a(1)=10081, a(n) = 2*a(n-1)-a(n-2). - _Harvey P. Dale_, Dec 16 2011
%F G.f.: (9977-9873*x)/(1-x)^2. - _Vincenzo Librandi_, Sep 10 2015
%t 104*Range[0,40]+9977 (* or *) LinearRecurrence[{2,-1},{9977,10081},40] (* _Harvey P. Dale_, Dec 16 2011 *)
%t CoefficientList[Series[(9977 - 9873 x)/(1 - x)^2, {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 10 2015 *)
%o (Magma) [104*n + 9977: n in [0..40]]; // _Vincenzo Librandi_, Sep 10 2015
%o (PARI) a(n)=104*n+9977 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A102127, A102358, A102369, A126979, A126980.
%K easy,nonn
%O 0,1
%A _Robert H Barbour_, Mar 20 2007, Jun 12 2007
|
