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

0,1

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).

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

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 *)

Prog

(Magma) [104*n + 9977: n in [0..40]]; // Vincenzo Librandi, Sep 10 2015
(PARI) a(n)=104*n+9977 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

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

Sequence in context: A031858 A254975 A182696 * A188790 A190832 A043528

Adjacent sequences: A126975 A126976 A126977 * A126979 A126980 A126981

Keyword

easy,nonn

Author

Robert H Barbour, Mar 20 2007, Jun 12 2007

Status

approved