A126978 a(n) = 104*n + 9977.

9977, 10081, 10185, 10289, 10393, 10497, 10601, 10705, 10809, 10913, 11017, 11121, 11225, 11329, 11433, 11537, 11641, 11745, 11849, 11953, 12057, 12161, 12265, 12369, 12473, 12577, 12681, 12785, 12889, 12993, 13097, 13201, 13305, 13409, 13513, 13617, 13721, 13825

Offset: 0

Author

Robert H Barbour, Mar 20 2007, Jun 12 2007

Keywords

• easy
• nonn

Comments

Langton's Ant Superhighway, the start point (9977th iteration, J. Propp) and the period length for the Superhighway (104).

Links

• B. D. Swan, Table of n, a(n) for n = 0..10000
• C. Langton, Studying Artificial Life with Cellular Automata, Physica D: Nonlinear Phenomena, Vol. 22, 1986, pp. 120-149.
• Ed Pegg Jr, 2D Turing Machines, 2004.
• James Propp, Further Ant-ics, Mathematical Intelligencer, Vol. 16, 1994, pp. 37-42.
• P. Sarkar, A Brief History of Cellular Automata, ACM Computing Surveys. Vol. 32, No. 1, Mar 01 2000, pp. 80-107.
• S. Wolfram, 2D Turing Machines.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A102127, A102358, A102369, A126979, A126980.

Programs

Magma

[104*n + 9977: n in [0..40]]; // Vincenzo Librandi, Sep 10 2015

Mathematica

104*Range[0,40]+9977 (* or *) LinearRecurrence[{2,-1},{9977,10081},40] (* Harvey P. Dale, Dec 16 2011 *)
CoefficientList[Series[(9977 - 9873 x)/(1 - x)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Sep 10 2015 *)

PARI

a(n)=104*n+9977 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(0)=9977, a(1)=10081, a(n) = 2*a(n-1) - a(n-2). - Harvey P. Dale, Dec 16 2011

G.f.: (9977 - 9873*x)/(1-x)^2. - Vincenzo Librandi, Sep 10 2015

E.g.f.: exp(x)*(9977 + 104*x). - Elmo R. Oliveira, Dec 08 2024