A126979 - OEIS

%I #19 Sep 08 2022 08:45:29

%S 233,257,281,305,329,353,377,401,425,449,473,497,521,545,569,593,617,

%T 641,665,689,713,737,761,785,809,833,857,881,905,929,953,977,1001,

%U 1025,1049,1073,1097,1121,1145,1169,1193,1217,1241,1265,1289,1313,1337,1361

%N a(n) = 24*n + 233.

%C 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.

%D P. Sakar, "A Brief History of Cellular Automata," ACM Computing Surveys, vol. 32, 2000.

%D S. Wolfram, A New Kind of Science, 1st ed. Il.: Wolfram Media Inc., 2002.

%H G. C. Greubel, <a href="/A126979/b126979.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F From _Chai Wah Wu_, May 30 2016: (Start)

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

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

%F E.g.f.: (233 + 24*x)*exp(x). - _G. C. Greubel_, May 28 2019

%t Table[24*n + 233, {n, 0, 60}] (* _Stefan Steinerberger_, Jun 17 2007 *)

%t LinearRecurrence[{2,-1}, {233,257}, 60] (* _G. C. Greubel_, May 28 2019 *)

%o (PARI) my(x='x+O('x^60)); Vec((233-209*x)/(1-x)^2) \\ _G. C. Greubel_, May 28 2019

%o (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

%o (Sage) ((233-209*x)/(1-x)^2).series(x, 60).coefficients(x, sparse=False) # _G. C. Greubel_, May 28 2019

%o (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

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

%K easy,nonn

%O 0,1

%A _Robert H Barbour_, Mar 20 2007, Jun 12 2007

%E More terms from _Stefan Steinerberger_, Jun 17 2007