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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This is the number of ON cells in a certain two-dimensional 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 odd-rule cellular automaton defined by OddRule 377 (see Ekhad-Sloane-Zeilberger "Odd-Rule 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 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

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[n-8] - 24f[n-7] + 164f[n-6] - 236f[n-5] + 145f[n-4] - 24f[n-3] - 16f[n-2] + 8f[n-1]; Table[Times @@ (f[Length[#]]&) /@ Select[ Split[ IntegerDigits[n, 2]], #[[1]] == 1&], {n, 0, 52}] (* Jean-Fran├žois Alcover, Jul 12 2017 *)

CROSSREFS

Cf. A255276.

Sequence in context: A077110 A098360 A133038 * 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

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Last modified March 23 18:13 EDT 2019. Contains 321433 sequences. (Running on oeis4.)