A255465 a(n) = A255464(2^n-1).

1, 6, 22, 90, 358, 1434, 5734, 22938, 91750, 367002, 1468006, 5872026, 23488102, 93952410, 375809638, 1503238554, 6012954214, 24051816858, 96207267430, 384829069722, 1539316278886, 6157265115546, 24629060462182, 98516241848730, 394064967394918, 1576259869579674

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 (3,4).

Crossrefs

Cf. A255464.

Programs

Mathematica

LinearRecurrence[{3, 4}, {1, 6}, 26] (* Jean-François Alcover, Sep 21 2017 *)

PARI

Vec((1+3*x) / ((1+x)*(1-4*x)) + O(x^30)) \\ Colin Barker, Feb 04 2017

Formula

G.f.: (1+3*x) / ((1+x)*(1-4*x)).

From Colin Barker, Feb 04 2017: (Start)

a(n) = (-2*(-1)^n + 7*4^n) / 5.

a(n) = 3*a(n-1) + 4*a(n-2) for n>1.

(End)