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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A164907. Inverse binomial transform of A057651.

Partial sums are in A083420.

REFERENCES

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, Preprint, 2015.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Catalog of 3X3 Odd Rule Cellular Automata

N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, 2015

Index entries for sequences related to cellular automata

FORMULA

a(n) = 4*a(n-1) for n > 1; a(0) = 1, a(1) = 6.

G.f.: (1+2*x)/(1-4*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^n-0^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^n-1), A247640.

Sequence in context: A255476 A253101 A169759 * A002023 A037505 A048179

Adjacent sequences:  A164905 A164906 A164907 * A164909 A164910 A164911

KEYWORD

nonn,changed

AUTHOR

Klaus Brockhaus, Aug 31 2009

STATUS

approved

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Last modified March 3 23:18 EST 2015. Contains 255178 sequences.