A253070 The subsequence A253069(2^n-1).

1, 6, 22, 82, 302, 1106, 4066, 14902, 54678, 200578, 735770, 2699182, 9901550, 36323050, 133247570, 488805718, 1793137798, 6577952882, 24130592458, 88520767614, 324729961566, 1191240790586, 4369952806274, 16030753627238, 58807285300086, 215728897446594, 791380812129402, 2903104763095054

Offset

0,2

Comments

A253069 is the Run Length Transform of this sequence.

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, 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, 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, 2015

Index entries for sequences related to cellular automata

Index entries for linear recurrences with constant coefficients, signature (3,3,-1,-6,10,-8,8).

Formula

G.f.: (1+2*x)*(1+x-x^2+x^3+2*x^5)/(1-3*x-3*x^2+x^3+6*x^4-10*x^5+8*x^6-8*x^7). - Doron Zeilberger, Feb 18 2015

Maple

OddCA2:=proc(f, M) local n, a, i, f2, g, p;
f2:=simplify(expand(f)) mod 2;
p:=1; g:=f2;
for n from 1 to M do p:=expand(p*g) mod 2; print(n, nops(p)); g:=expand(g^2) mod 2; od:
return;
end;
f:=1/x+1+x+x/y+y/x+x*y;
OddCA2(f, 10);

Mathematica

LinearRecurrence[{3, 3, -1, -6, 10, -8, 8}, {1, 6, 22, 82, 302, 1106, 4066}, 28] (* Jean-François Alcover, Nov 27 2017 *)

Prog

(PARI) Vec(-(2*x+1)*(2*x^5+x^3-x^2+x+1)/(8*x^7-8*x^6+10*x^5-6*x^4-x^3+3*x^2+3*x-1) + O(x^30)) \\ Colin Barker, Jul 16 2015

Crossrefs

Cf. A253067, A253068, A253069.

Sequence in context: A111566 A200052 A051945 * A255461 A003699 A047124

Adjacent sequences: A253067 A253068 A253069 * A253071 A253072 A253073

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 29 2015

Extensions

a(11) and a(12) (Maple on a 32 GB machine) from R. J. Mathar, Feb 04 2015

a(13) onwards from Doron Zeilberger, Feb 18 2015 (the terms previously listed were wrong). - N. J. A. Sloane, Feb 19 2015

Status

approved