

A255275


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


1



1, 8, 8, 28, 8, 64, 28, 128, 8, 64, 64, 224, 28, 224, 128, 480, 8, 64, 64, 224, 64, 512, 224, 1024, 28, 224, 224, 784, 128, 1024, 480, 2008, 8, 64, 64, 224, 64, 512, 224, 1024, 64, 512, 512, 1792, 224, 1792, 1024, 3840, 28, 224, 224, 784, 224
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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 377 (see EkhadSloaneZeilberger "OddRule Cellular Automata on the Square Grid" link).


LINKS

Table of n, a(n) for n=0..52.
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 A255276.


EXAMPLE

Here is the neighborhood f:
[0, X, X]
[X, X, X]
[X, X, X]
which contains a(1) = 8 ON cells.


MATHEMATICA

(* f = A255276 *) f[0]=1; f[1]=8; f[2]=28; f[3]=128; f[4]=480; f[5]=2008; f[6]=7776; f[n_] := f[n] = 32f[n8]  24f[n7] + 164f[n6]  236f[n5] + 145f[n4]  24f[n3]  16f[n2] + 8f[n1]; Table[Times @@ (f[Length[#]]&) /@ Select[ Split[ IntegerDigits[n, 2]], #[[1]] == 1&], {n, 0, 52}] (* JeanFrançois Alcover, Jul 12 2017 *)


CROSSREFS

Cf. A255276.
Sequence in context: A133038 A339734 A341834 * A253104 A122858 A143336
Adjacent sequences: A255272 A255273 A255274 * A255276 A255277 A255278


KEYWORD

nonn


AUTHOR

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


STATUS

approved



