This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A164908 a(n) = (3*4^n - 0^n)/2. 6
 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. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 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, 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, 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 linear recurrences with constant coefficients, signature (4). 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)/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] ]; (PARI) a(n)=3*4^n\2 \\ Charles R Greathouse IV, Oct 12 2015 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: A303390 A253101 A169759 * A002023 A290911 A037505 Adjacent sequences:  A164905 A164906 A164907 * A164909 A164910 A164911 KEYWORD nonn,easy AUTHOR Klaus Brockhaus, Aug 31 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 23 18:13 EDT 2019. Contains 321433 sequences. (Running on oeis4.)