OFFSET
0,1
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).
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)
MATHEMATICA
Range[4, 1000, 13] (* Vladimir Joseph Stephan Orlovsky, May 31 2011 *)
PROG
(Magma) [13*n+4: n in [0..60]]; // G. C. Greubel, May 31 2024
(SageMath) [13*n+4 for n in range(61)] # G. C. Greubel, May 31 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Robert H Barbour, Apr 01 2007
EXTENSIONS
Edited by N. J. A. Sloane, May 10 2007
STATUS
approved