

A164908


a(n) = (3*4^n  0^n)/2.


5



1, 6, 24, 96, 384, 1536, 6144, 24576, 98304, 393216, 1572864, 6291456, 25165824, 100663296, 402653184, 1610612736, 6442450944, 25769803776, 103079215104, 412316860416, 1649267441664, 6597069766656, 26388279066624
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OFFSET

0,2


COMMENTS

Binomial transform of A164907. Inverse binomial transform of A057651.
Partial sums are in A083420.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, A MetaAlgorithm for Creating Fast Algorithms for Counting ON Cells in OddRule Cellular Automata, arXiv:1503.01796, 2015; see also the Accompanying Maple Package.
Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger, OddRule Cellular Automata on the Square Grid, arXiv:1503.04249, 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
Index entries for sequences related to cellular automata


FORMULA

a(n) = 4*a(n1) for n > 1; a(0) = 1, a(1) = 6.
G.f.: (1+2*x)/(14*x).


MATHEMATICA

a[n_]:=(MatrixPower[{{2, 2}, {2, 2}}, n].{{2}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2010 *)
Join[{1}, (3*4^Range[25])/2] (* or *) Join[{1}, NestList[4#&, 6, 25]] (* Harvey P. Dale, Feb 14 2012 *)


PROG

(MAGMA) [ (3*4^n0^n)/2: n in [0..22] ];


CROSSREFS

Equals 1 followed by A002023 (6*4^n). Essentially the same as A084509.
Cf. A164907, A057651, A083420 (2*4^n1), A247640.
Sequence in context: A255476 A253101 A169759 * A002023 A037505 A048179
Adjacent sequences: A164905 A164906 A164907 * A164909 A164910 A164911


KEYWORD

nonn


AUTHOR

Klaus Brockhaus, Aug 31 2009


STATUS

approved



