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 A003954 Expansion of g.f.: (1+x)/(1-11*x). 57
 1, 12, 132, 1452, 15972, 175692, 1932612, 21258732, 233846052, 2572306572, 28295372292, 311249095212, 3423740047332, 37661140520652, 414272545727172, 4556998002998892, 50126978032987812 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Coordination sequence for infinite tree with valency 12. The n-th term of the coordination sequence of the infinite tree with valency 2m is the same as the number of reduced words of size n in the free group on m generators. In the five sequences A003946, A003948, A003950, A003952, A003954 m is 2, 3, 4, 5, 6 . - Avi Peretz (njk(AT)netvision.net.il), Feb 23 2001 and Ola Veshta (olaveshta(AT)my-deja.com), Mar 30 2001. For n>=1, a(n) equals the numbers of words of length n-1 on alphabet {0,1,...,11} with no two adjacent letters identical. - Milan Janjic, Jan 31 2015 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..900 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 313 Index entries for linear recurrences with constant coefficients, signature (11). FORMULA a(n) = Sum_{k=0..n} A029653(n, k)*x^k for x = 10. - Philippe Deléham, Jul 10 2005 G.f.: (1+x)/(1-11*x). The Hankel transform of this sequence is [1,-12,0,0,0,0,0,0,0,...]. - Philippe Deléham, Nov 21 2007 a(0) = 1; for n>0, a(n) = 12*11^(n-1). - Vincenzo Librandi, Nov 18 2010 a(0) = 1, a(1)=12, a(n) = 11*a(n-1). - Vincenzo Librandi, Dec 10 2012 MAPLE k:=12; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # modified by G. C. Greubel, Sep 24 2019 MATHEMATICA Join[{1}, 12*11^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *) CoefficientList[Series[(1+x)/(1-11x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2012 *) PROG (MAGMA)  cat [12*11^(n-1): n in [1..20]]; // Vincenzo Librandi, Dec 11 2012 (PARI) a(n)=12*11^n\11 \\ Charles R Greathouse IV, Aug 14 2015 (Sage) +[12*11^(n-1) for n in (1..20)] # G. C. Greubel, Sep 23 2019 (GAP) Concatenation(, List([1..20], n-> 12*11^(n-1) )); # G. C. Greubel, Sep 23 2019 CROSSREFS Cf. A003952, A003953. Sequence in context: A167113 A167665 A167916 * A168689 A168737 A168785 Adjacent sequences:  A003951 A003952 A003953 * A003955 A003956 A003957 KEYWORD nonn,easy AUTHOR EXTENSIONS Edited by N. J. A. Sloane, Dec 04 2009 STATUS approved

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Last modified November 14 17:24 EST 2019. Contains 329126 sequences. (Running on oeis4.)