A127547 a(n) = 13*n + 4.

4, 17, 30, 43, 56, 69, 82, 95, 108, 121, 134, 147, 160, 173, 186, 199, 212, 225, 238, 251, 264, 277, 290, 303, 316, 329, 342, 355, 368, 381, 394, 407, 420, 433, 446, 459, 472, 485, 498, 511, 524, 537, 550, 563, 576, 589, 602, 615, 628, 641, 654, 667, 680, 693, 706, 719

Offset: 0

Author

Robert H Barbour, Apr 01 2007

Keywords

• easy
• nonn

Comments

Superhighway created by 'LQTL Ant' L90R90L45R45 from iteration 4 where the Ant moves in a 'Moore neighborhood' (nine cells), the L indicates a left turn, the R a right turn, and the numerical value is the size of the turn (in degrees) at each iteration.

Ant Farm algorithm available from Robert H Barbour.

References

• P. Sakar, "A Brief History of Cellular Automata," ACM Computing Surveys, vol. 32, pp. 80-107, 2000.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• C. Langton, Studying Artificial Life with Cellular Automata, Physica D: Nonlinear Phenomena, vol. 22, pp. 120-149, 1986.
• James Propp, Further Ant-ics, Mathematical Intelligencer, 16 pp. 37-42, 1994.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

A subsequence of A092464.

Cf. A126979, A126980.

Sequences of the form 13*n+q: A008595 (q=0), A190991 (q=1), A153080 (q=2), this sequence (q=4), A154609 (q=5), A186113 (q=6), A269044 (q=7), A269100 (q=11).

Programs

Magma

[13*n+4: n in [0..60]]; // G. C. Greubel, May 31 2024

Mathematica

Range[4,1000,13] (* Vladimir Joseph Stephan Orlovsky, May 31 2011 *)

SageMath

[13*n+4 for n in range(61)] # G. C. Greubel, May 31 2024

Formula

From Elmo R. Oliveira, Mar 21 2024: (Start)

G.f.: (4+9*x)/(1-x)^2.

E.g.f.: (4 + 13*x)*exp(x).

a(n) = 2*a(n-1) - a(n-2) for n >= 2. (End)

Extensions

Edited by N. J. A. Sloane, May 10 2007