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A246030 a(n) = (5*2^(2*n)+(-2)^(n+1))/3. 3
1, 8, 24, 112, 416, 1728, 6784, 27392, 109056, 437248, 1746944, 6991872, 27959296, 111853568, 447381504, 1789591552, 7158235136, 28633202688, 114532286464, 458130194432, 1832518680576, 7330078916608, 29320307277824, 117281245888512, 469124949999616, 1876499867107328, 7505999334211584 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Essentially 8 times A083424.
Equals A160239(2^n). - N. J. A. Sloane, Oct 04 2014
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, 2015
FORMULA
a(0)=1, a(1)=8; thereafter a(n)=2*a(n-1)+8*a(n-2).
G.f.: (1+6*x)/(1-2*x-8*x^2).
a(n) = A001045(n+2)^2 - A001045(n)^2. - J. Conrad, Apr 05 2023
MATHEMATICA
CoefficientList[Series[(1 + 6 x) / (1 - 2 x - 8 x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 20 2015 *)
PROG
(Magma) I:=[1, 8]; [n le 2 select I[n] else 2*Self(n-1)+8*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Feb 20 2015
CROSSREFS
Sequence in context: A267326 A063515 A220706 * A010566 A305224 A182068
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Aug 15 2014
STATUS
approved

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Last modified March 28 12:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)