A255463 a(n) = 3*4^n - 2*3^n.
1, 6, 30, 138, 606, 2586, 10830, 44778, 183486, 747066, 3027630, 12228618, 49268766, 198137946, 795740430, 3192527658, 12798808446, 51281327226, 205383589230, 822309197898, 3291561314526, 13173218826906, 52713796014030, 210917946175338, 843860071059006, 3376005143308986, 13505715150454830
Offset: 0
Links
- Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, A Meta-Algorithm for Creating Fast Algorithms for Counting ON Cells in Odd-Rule Cellular Automata, arXiv:1503.01796 [math.CO], 2015; see also the Accompanying Maple Package.
- Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, Odd-Rule Cellular Automata on the Square Grid, arXiv:1503.04249 [math.CO], 2015.
- N. J. A. Sloane, On the No. of ON Cells in Cellular Automata, Video of talk in Doron Zeilberger's Experimental Math Seminar at Rutgers University, Feb. 05 2015: Part 1, Part 2
- N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015
- Index entries for sequences related to cellular automata
- Index entries for linear recurrences with constant coefficients, signature (7,-12).
Crossrefs
Programs
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Magma
[3*4^n-2*3^n: n in [0..30]]; // Vincenzo Librandi, May 04 2015
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Mathematica
Table[3 4^n - 2 3^n, {n, 0, 30}] (* Vincenzo Librandi, May 04 2015 *) -
PARI
a(n)=3*4^n-2*3^n \\ M. F. Hasler, May 04 2015
Formula
G.f.: (1-x)/((1-3*x)*(1-4*x)).
a(n+1) = 7*a(n) - 12*a(n-1) with a(0)=1, a(1)=6.
a(n) = A255462(2^n-1).
E.g.f.: exp(3*x)*(3*exp(x) - 2). - Stefano Spezia, Nov 15 2023
Extensions
Simpler definition from N. J. A. Sloane, Mar 10 2015
Comments