A255301 a(n) = A255300(2^k-1).

1, 4, 16, 56, 196, 680, 2348, 8096, 27892, 96056, 330748, 1138768, 3920644, 13498088, 46471180, 159990272, 550811156, 1896319640, 6528602140, 22476505520, 77381536036, 266407155784, 917179667500, 3157642420064, 10871049557044, 37426567849976, 128851218332732, 443605636686608, 1527233994485572

Offset

0,2

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 (4,-1,-2,-4).

Formula

G.f.: (1-x)*(1+x+2*x^2) / (1-4*x+x^2+2*x^3+4*x^4).

a(n) = 4*a(n-1) - a(n-2) - 2*a(n-3) - 4*a(n-4) for n>3. - Colin Barker, Feb 04 2017

Mathematica

LinearRecurrence[{4, -1, -2, -4}, {1, 4, 16, 56}, 30] (* Jean-François Alcover, Oct 10 2018 *)

Prog

(PARI) Vec((1-x)*(1+x+2*x^2) / (1-4*x+x^2+2*x^3+4*x^4) + O(x^30)) \\ Colin Barker, Feb 04 2017

Crossrefs

Cf. A255300.

Sequence in context: A025182 A057585 A333107 * A097128 A006079 A218263

Adjacent sequences: A255298 A255299 A255300 * A255302 A255303 A255304

Keyword

nonn,easy

Author

N. J. A. Sloane and Doron Zeilberger, Feb 23 2015

Status

approved