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 A003950 G.f.: (1+x)/(1-7*x). 58
 1, 8, 56, 392, 2744, 19208, 134456, 941192, 6588344, 46118408, 322828856, 2259801992, 15818613944, 110730297608, 775112083256, 5425784582792, 37980492079544, 265863444556808, 1861044111897656, 13027308783283592, 91191161482985144, 638338130380896008 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Coordination sequence for infinite tree with valency 8. 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 number of words of length n on the alphabet {0,1,...,7} with no two adjacent letters identical. - Milan Janjic, Jan 31 2015 [Corrected by David Nacin, May 31 2017] a(n) is the number of octonary sequences of length n such that no two consecutive terms have distance 4. - David Nacin, May 31 2017 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 309 A. M. Nemirovsky et al., Marriage of exact enumeration and 1/d expansion methods: lattice model of dilute polymers, J. Statist. Phys., 67 (1992), 1083-1108. Index entries for linear recurrences with constant coefficients, signature (7). FORMULA a(n) = Sum_{ 0<=k<=n } A029653(n, k)*x^k for x = 6. - Philippe Deléham, Jul 10 2005 a(n) = 8*7^(n-1) for n>=1, a(0)=1 . G.f.: (1+x)/(1-7x). The Hankel transform of this sequence is [1,-8,0,0,0,0,0,0,0,0,...]. - Philippe Deléham, Nov 21 2007 a(0)=1, a(1)=8, a(n) = 7*a(n-1). - Vincenzo Librandi, Dec 10 2012 MAPLE k := 8; if n = 0 then 1 else k*(k-1)^(n-1); fi; MATHEMATICA Join[{1}, 8*7^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *) CoefficientList[Series[(1 + x)/(1 - 7*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2012 *) PROG (MAGMA) [1] cat [8*7^(n-1): n in [1..25]]; // Vincenzo Librandi, Dec 11 2012 (PARI) a(n)=if(n, 8*7^(n-1), 1) \\ Charles R Greathouse IV, Mar 22 2016 CROSSREFS Cf. A003948, A003949, A003951. Sequence in context: A170593 A170641 A170689 * A252701 A033134 A126985 Adjacent sequences:  A003947 A003948 A003949 * A003951 A003952 A003953 KEYWORD nonn,walk,easy AUTHOR EXTENSIONS Edited by N. J. A. Sloane, Dec 04 2009 STATUS approved

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