A253102 - OEIS

%I #16 Sep 15 2018 05:29:08

%S 1,27,27,125,27,729,125,1331,27,729,729,3375,125,3375,1331,9261,27,

%T 729,729,3375,729,19683,3375,35937,125,3375,3375,15625,1331,35937,

%U 9261,79507,27,729,729,3375,729,19683,3375,35937,729,19683,19683,91125,3375,91125,35937,250047,125,3375,3375,15625

%N a(n) = A071053(n)^3.

%C Number of ON cells at n-th generation of 3-D CA defined by generalization of Rule 150, starting with a single ON cell at generation 0.

%C Number of odd coefficients in ((1/x+1+x)*(1/y+1+y)*(1/z+1+z))^n.

%C Run length transform of A253103.

%H 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: <a href="https://vimeo.com/119073818">Part 1</a>, <a href="https://vimeo.com/119073819">Part 2</a>

%H N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168 [math.CO], 2015.

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%t a71053[n_] := Total[CoefficientList[(x^2 + x + 1)^n, x, Modulus -> 2]];

%t Table[a71053[n]^3, {n, 0, 51}] (* _Jean-François Alcover_, Sep 15 2018 *)

%Y Cf. A071053, A246035, A253103.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Feb 20 2015