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
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).
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
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