

A255281


Number of odd terms in f^n, where f = (1/x+1+x)*(1/y+1+y)y/xx.


2



1, 7, 7, 31, 7, 49, 31, 127, 7, 49, 49, 217, 31, 217, 127, 511, 7, 49, 49, 217, 49, 343, 217, 889, 31, 217, 217, 961, 127, 889, 511, 2031, 7, 49, 49, 217, 49, 343, 217, 889, 49, 343, 343, 1519, 217, 1519, 889, 3577, 31, 217, 217, 961, 217, 1519
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OFFSET

0,2


COMMENTS

This is the number of ON cells in a certain twodimensional cellular automaton in which the neighborhood of a cell is defined by f, and in which a cell is ON iff there were an odd number of ON cells in the neighborhood at the previous generation.
This is the oddrule cellular automaton defined by OddRule 367 (see EkhadSloaneZeilberger "OddRule Cellular Automata on the Square Grid" link).


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..8191
Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, A MetaAlgorithm for Creating Fast Algorithms for Counting ON Cells in OddRule Cellular Automata, arXiv:1503.01796, 2015; see also the Accompanying Maple Package.
Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, OddRule 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


FORMULA

This is the Run Length Transform of A255282.


EXAMPLE

Here is the neighborhood f:
[0, X, X]
[X, X, 0]
[X, X, X]
which contains a(1) = 7 ON cells.


MATHEMATICA

(* f = A255282 *) f[0]=1; f[1]=7; f[2]=31; f[3]=127; f[4]=511; f[5]=2031; f[6]=8043; f[7]=31735; f[8]=125063; f[n_] := f[n] = 10 f[n10] + 22 f[n9]  11 f[n8] + 31 f[n7]  24 f[n6] + 3 f[n5] + 18 f[n4]  21 f[n3] + 5 f[n1]; Table[Times @@ (f[Length[#]]&) /@ Select[ Split[ IntegerDigits[n, 2]], #[[1]] == 1&], {n, 0, 53}] (* JeanFrançois Alcover, Jul 12 2017 *)


CROSSREFS

Cf. A255282.
Sequence in context: A246039 A186142 A188274 * A255283 A140252 A095343
Adjacent sequences: A255278 A255279 A255280 * A255282 A255283 A255284


KEYWORD

nonn


AUTHOR

N. J. A. Sloane and Doron Zeilberger, Feb 19 2015


STATUS

approved



