A255474 a(n) = A255473(2^n-1).

1, 6, 24, 88, 336, 1280, 4928, 19072, 74240, 290304, 1139712, 4489216, 17731584, 70197248, 278429696, 1106083840, 4399628288, 17518559232, 69815500800, 278424715264, 1110989340672, 4435189170176, 17712382214144, 70757707153408, 282733687341056, 1129973180006400

Offset

0,2

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,-4,-16).

Formula

G.f.: (1-8*x^2-16*x^3) / ((1-4*x)*(1-2*x-4*x^2)).

From Colin Barker, Feb 05 2017: (Start)

a(n) = 4^n + (-(1-sqrt(5))^(1+n) + (1+sqrt(5))^(1+n)) / (2*sqrt(5)) for n>0.

a(n) = 6*a(n-1) - 4*a(n-2) - 16*a(n-3) for n>3.

(End)

Prog

(PARI) Vec((1-8*x^2-16*x^3) / ((1-4*x)*(1-2*x-4*x^2)) + O(x^30)) \\ Colin Barker, Feb 05 2017

Crossrefs

Cf. A255473.

Sequence in context: A271789 A121532 A025472 * A249976 A181618 A002919

Adjacent sequences: A255471 A255472 A255473 * A255475 A255476 A255477

Keyword

nonn,easy

Author

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

Status

approved