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A255463 a(n) = 3*4^n-2*3^n. 6
1, 6, 30, 138, 606, 2586, 10830, 44778, 183486, 747066, 3027630, 12228618, 49268766, 198137946, 795740430, 3192527658, 12798808446, 51281327226, 205383589230, 822309197898, 3291561314526, 13173218826906, 52713796014030, 210917946175338, 843860071059006, 3376005143308986, 13505715150454830 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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 (7,-12).

FORMULA

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

a(n+1) = 7*a(n)-12*a(n-1) with a(0)=1, a(1)=6.

a(n) = A255462(2^n-1).

MATHEMATICA

Table[3 4^n - 2 3^n, {n, 0, 30}] (* Vincenzo Librandi, May 04 2015 *)

PROG

(PARI) a(n)=3*4^n-2*3^n \\ M. F. Hasler, May 04 2015

(MAGMA) [3*4^n-2*3^n: n in [0..30]]; // Vincenzo Librandi, May 04 2015

CROSSREFS

Cf. A255462.

First differences of 4^n-3^n = A005061(n). See A257285 - A257289 for first differences of 5^n-4^n, ..., 9^n-8^n. - M. F. Hasler, May 04 2015

Sequence in context: A030280 A034545 A002920 * A192208 A001334 A125316

Adjacent sequences:  A255460 A255461 A255462 * A255464 A255465 A255466

KEYWORD

nonn,easy

AUTHOR

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

EXTENSIONS

Simpler definition from N. J. A. Sloane, Mar 10 2015

STATUS

approved

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Last modified November 13 19:25 EST 2018. Contains 317149 sequences. (Running on oeis4.)