A126979 a(n) = 24*n + 233.

233, 257, 281, 305, 329, 353, 377, 401, 425, 449, 473, 497, 521, 545, 569, 593, 617, 641, 665, 689, 713, 737, 761, 785, 809, 833, 857, 881, 905, 929, 953, 977, 1001, 1025, 1049, 1073, 1097, 1121, 1145, 1169, 1193, 1217, 1241, 1265, 1289, 1313, 1337, 1361

Offset: 0

Author

Robert H Barbour, Mar 20 2007, Jun 12 2007

Keywords

• easy
• nonn

Comments

Superhighway created by 'LQTL Ant' L45R135L45R135 from iteration 233 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 turn angle in degrees.

References

• P. Sakar, "A Brief History of Cellular Automata," ACM Computing Surveys, vol. 32, 2000.
• S. Wolfram, A New Kind of Science, 1st ed. Il.: Wolfram Media Inc., 2002.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A031041, A017581, A126978, A126980. Has many terms in common with A031041.

Programs

GAP

a:=[233, 257];; for n in [3..60] do a[n]:=2*a[n-1]-a[n-2]; od; a; # G. C. Greubel, May 28 2019

Magma

I:=[233, 257]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..60]]; // G. C. Greubel, May 28 2019

Mathematica

Table[24*n + 233, {n, 0, 60}] (* Stefan Steinerberger, Jun 17 2007 *)
LinearRecurrence[{2,-1}, {233,257}, 60] (* G. C. Greubel, May 28 2019 *)

PARI

my(x='x+O('x^60)); Vec((233-209*x)/(1-x)^2) \\ G. C. Greubel, May 28 2019

Sage

((233-209*x)/(1-x)^2).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, May 28 2019

Formula

From Chai Wah Wu, May 30 2016: (Start)

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

G.f.: (233 - 209*x)/(1 - x)^2. (End)

E.g.f.: (233 + 24*x)*exp(x). - G. C. Greubel, May 28 2019

Extensions

More terms from Stefan Steinerberger, Jun 17 2007