A253101 a(n) = A253100(2^n-1).
1, 6, 24, 96, 372, 1416, 5340, 20040, 75012, 280392, 1047324, 3910440, 14597508, 54485736, 203357724, 758969736, 2832570372, 10571410056, 39453266460, 147242049000, 549515715972, 2050822387752, 7653776980764, 28564291826760, 106603402909188, 397849344975816, 1484794027325724, 5541326864990376
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- 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 (6,-9,2).
Crossrefs
Cf. A253100.
Programs
-
Mathematica
Join[{1}, LinearRecurrence[{6, -9, 2}, {6, 24, 96}, 30]] (* Jean-François Alcover, Jan 09 2019 *) -
PARI
Vec((1-3*x^2+4*x^3) / ((1-2*x)*(1-4*x+x^2)) + O(x^30)) \\ Colin Barker, Feb 04 2017
Formula
G.f.: (1-3*x^2+4*x^3) / ((1-2*x)*(1-4*x+x^2)).
From Colin Barker, Feb 04 2017: (Start)
a(n) = -2^n + 2*(2-sqrt(3))^n + 2*(2+sqrt(3))^n for n>0.
a(n) = 6*a(n-1) - 9*a(n-2) + 2*a(n-3) for n>3.
(End)
Extensions
Typo in the definition corrected by Antti Karttunen, Nov 18 2016