A255299 A255298(2^n-1).

1, 4, 16, 58, 204, 714, 2492, 8682, 30228, 105226, 366276, 1274922, 4437692, 15446554, 53765916, 187147146, 651418116, 2267444842, 7892485300, 27472040138, 95624259340, 332847482970, 1158570537292, 4032735032490, 14037083980308, 48860072772074, 170071413502180, 591982043090090, 2060562279111580, 7172374493538586, 24965494321148156, 86899520830961866, 302478557946941732, 1052862859805769450, 3664789362535367700

Offset

0,2

Links

Table of n, a(n) for n=0..34.

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

Formula

G.f.: (1-x)*(1-x+x^2-x^3-4*x^4+2*x^5-2*x^6)/(1-6*x+10*x^2-4*x^3-3*x^4+12*x^5-20*x^6+10*x^7-4*x^8).

Mathematica

A255299[n_] := SeriesCoefficient[(1 - x)*(1 - x + x^2 - x^3 - 4*x^4 + 2*x^5 - 2*x^6)/(1 - 6*x + 10*x^2 - 4*x^3 - 3*x^4 + 12*x^5 - 20*x^6 + 10*x^7 - 4*x^8), {x, 0, n}]; Array[A255299, 35, 0] (* JungHwan Min, Sep 29 2016 *)
A255299L[n_] := CoefficientList[Series[(1 - x)*(1 - x + x^2 - x^3 - 4*x^4 + 2*x^5 - 2*x^6)/(1 - 6*x + 10*x^2 - 4*x^3 - 3*x^4 + 12*x^5 - 20*x^6 + 10*x^7 - 4*x^8), {x, 0, n}], x]; A255299L[34] (* JungHwan Min, Sep 29 2016 *)

Crossrefs

Cf. A255298.

Sequence in context: A168583 A092688 A267466 * A123889 A180143 A224128

Adjacent sequences: A255296 A255297 A255298 * A255300 A255301 A255302

Keyword

nonn

Author

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

Status

approved