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A255463 a(n) = 3*4^n - 2*3^n. 7
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
COMMENTS
a(n-1) is also the number of n-digit numbers whose largest decimal digit is 3. - Stefano Spezia, Nov 15 2023
LINKS
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
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).
E.g.f.: exp(3*x)*(3*exp(x) - 2). - Stefano Spezia, Nov 15 2023
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, A257286, A257287, A257288, 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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Simpler definition from N. J. A. Sloane, Mar 10 2015
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)