This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A063759 Spherical growth series for modular group. 8
 1, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096, 6144, 8192, 12288, 16384, 24576, 32768, 49152, 65536, 98304, 131072, 196608, 262144, 393216, 524288, 786432, 1048576, 1572864, 2097152 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also number of sequences S of length n with entries in {1,..,q} where q = 3, satisfying the condition that adjacent terms differ in absolute value by exactly 1, see examples. - W. Edwin Clark, Oct 17 2008 REFERENCES P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 156. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (0,2) FORMULA G.f.: (1+3*x+2*x^2)/(1-2*x^2). a(n) = 2*a(n-2), n>2. - Harvey P. Dale, Oct 22 2011 a(2*n) = A151821(n+1); a(2*n+1) = A007283(n). - Reinhard Zumkeller, Dec 16 2013 EXAMPLE For n = 2 the a(2) = 4 sequences are (1,2),(2,1),(2,3),(3,2). - W. Edwin Clark, Oct 17 2008 From Joerg Arndt, Nov 23 2012: (Start) There are a(6) = 16 such words of length 6: [ 1]   [ 1 2 1 2 1 2 ] [ 2]   [ 1 2 1 2 3 2 ] [ 3]   [ 1 2 3 2 1 2 ] [ 4]   [ 1 2 3 2 3 2 ] [ 5]   [ 2 1 2 1 2 1 ] [ 6]   [ 2 1 2 1 2 3 ] [ 7]   [ 2 1 2 3 2 1 ] [ 8]   [ 2 1 2 3 2 3 ] [ 9]   [ 2 3 2 1 2 1 ] [10]   [ 2 3 2 1 2 3 ] [11]   [ 2 3 2 3 2 1 ] [12]   [ 2 3 2 3 2 3 ] [13]   [ 3 2 1 2 1 2 ] [14]   [ 3 2 1 2 3 2 ] [15]   [ 3 2 3 2 1 2 ] [16]   [ 3 2 3 2 3 2 ] (End) MATHEMATICA CoefficientList[Series[(1+3*x+2*x^2)/(1-2*x^2), {x, 0, 40}], x](* Jean-François Alcover, Mar 21 2011 *) Join[{1}, Transpose[NestList[{Last[#], 2First[#]}&, {3, 4}, 40]][[1]]] (* Harvey P. Dale, Oct 22 2011 *) PROG (Haskell) import Data.List (transpose) a063759 n = a063759_list !! n a063759_list = concat \$ transpose [a151821_list, a007283_list] -- Reinhard Zumkeller, Dec 16 2013 (PARI) a(n)=([0, 1; 2, 0]^n*[1; 3])[1, 1] \\ Charles R Greathouse IV, Feb 09 2017 CROSSREFS Cf. A054886, A029744. The sequence (ternary strings) seems to be related to A029744 and A090989. Sequence in context: A147606 A279083 A085147 * A163978 A145751 A277099 Adjacent sequences:  A063756 A063757 A063758 * A063760 A063761 A063762 KEYWORD nonn,nice,easy AUTHOR N. J. A. Sloane, Aug 14 2001 EXTENSIONS Information from A145751 included by Joerg Arndt, Dec 03 2012 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.