A253102 a(n) = A071053(n)^3.

1, 27, 27, 125, 27, 729, 125, 1331, 27, 729, 729, 3375, 125, 3375, 1331, 9261, 27, 729, 729, 3375, 729, 19683, 3375, 35937, 125, 3375, 3375, 15625, 1331, 35937, 9261, 79507, 27, 729, 729, 3375, 729, 19683, 3375, 35937, 729, 19683, 19683, 91125, 3375, 91125, 35937, 250047, 125, 3375, 3375, 15625

Offset: 0

Author

N. J. A. Sloane, Feb 20 2015

Keywords

• nonn

Comments

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.

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

Run length transform of A253103.

Links

• 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 [math.CO], 2015.
• Index entries for sequences related to cellular automata

Crossrefs

Cf. A071053, A246035, A253103.

Programs

Mathematica

a71053[n_] := Total[CoefficientList[(x^2 + x + 1)^n, x, Modulus -> 2]];
Table[a71053[n]^3, {n, 0, 51}] (* Jean-François Alcover, Sep 15 2018 *)