A255471 a(n) = A255470(2^n-1).

1, 6, 24, 100, 396, 1596, 6364, 25500, 101916, 407836, 1631004, 6524700, 26097436, 104392476, 417564444, 1670268700, 6681052956, 26724255516, 106896934684, 427587913500, 1710351304476, 6841405916956, 27365622269724, 109462491875100, 437849961907996, 1751399858816796, 7005599412897564, 28022397696329500, 112089590695839516

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 (3,6,-8).

Crossrefs

Cf. A255470.

Programs

PARI

Vec((1+3*x) / ((1-x)*(1+2*x)*(1-4*x)) + O(x^30)) \\ Colin Barker, Feb 04 2017

Formula

G.f.: (1+3*x)/((1-x)*(1+2*x)*(1-4*x)).

From Colin Barker, Feb 04 2017: (Start)

a(n) = (-4 - (-2)^n + 7*2^(1+2*n)) / 9.

a(n) = 3*a(n-1) + 6*a(n-2) - 8*a(n-3) for n>2.

(End)