A255459 a(n) = A255458(2^n-1).

1, 5, 25, 101, 361, 1205, 3865, 12101, 37321, 114005, 346105, 1046501, 3155881, 9500405, 28566745, 85831301, 257756041, 773792405, 2322425785, 6969374501, 20912317801, 62745342005, 188252803225, 564791964101, 1694443001161, 5083463221205, 15250658099065

Offset: 0

Author

N. J. A. Sloane and Doron Zeilberger, Feb 23 2015

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• 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 [math.CO], 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 [math.CO], 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 [math.CO], 2015.
• Index entries for sequences related to cellular automata
• Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Crossrefs

Cf. A255458.

Programs

Mathematica

LinearRecurrence[{6, -11, 6}, {1, 5, 25}, 30] (* Jean-François Alcover, Jan 09 2019 *)

PARI

Vec((1-x+6*x^2) / ((1-x)*(1-2*x)*(1-3*x)) + O(x^30)) \\ Colin Barker, Feb 03 2017

Formula

G.f.: (1-x+6*x^2) / ((1-x)*(1-2*x)*(1-3*x)).

From Colin Barker, Feb 03 2017: (Start)

a(n) = (3 - 2^(3+n) + 2*3^(1+n)).

a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>2.

(End)