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 A003951 Expansion of g.f.: (1+x)/(1-8*x). 56
 1, 9, 72, 576, 4608, 36864, 294912, 2359296, 18874368, 150994944, 1207959552, 9663676416, 77309411328, 618475290624, 4947802324992, 39582418599936, 316659348799488, 2533274790395904, 20266198323167232, 162129586585337856, 1297036692682702848 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Coordination sequence for infinite tree with valency 9. Binomial transform is {1, 10, 91, 820, 7381, ...}, see A002452. - Philippe Deléham, Jul 22 2005 a(n) equals the number of words of length n on alphabet {0,1,...,8} with no two adjacent letters identical. - Milan Janjic, Jan 31 2015 [Corrected by David Nacin, May 31 2017] LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 310 Index entries for linear recurrences with constant coefficients, signature (8). FORMULA a(n) = Sum_{k=0..n} A029653(n, k)*x^k for x = 7. - Philippe Deléham, Jul 10 2005 a(0) = 1; for n>0, a(n) = 9*8^(n-1). - Vincenzo Librandi, Nov 18 2010 a(0) = 1, a(1) = 9, a(n) = 8*a(n-1). - Vincenzo Librandi, Dec 10 2012 E.g.f.: (9*exp(8*x) -1)/8. - G. C. Greubel, Sep 24 2019 MAPLE k:=9; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # modified by G. C. Greubel, Sep 24 2019 MATHEMATICA Join[{1}, 9*8^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *) CoefficientList[Series[(1+x)/(1-8*x), {x, 0, 25}], x] (* Vincenzo Librandi, Dec 10 2012 *) PROG (MAGMA) [1] cat [9*8^(n-1): n in [1..25]]; // Vincenzo Librandi, Dec 11 2012 (PARI) a(n)=if(n, 9*8^n/8, 1) \\ Charles R Greathouse IV, Mar 22 2016 (Sage) k=9; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 24 2019 (GAP) k:=9;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019 CROSSREFS Cf. A003945. Sequence in context: A170594 A170642 A170690 * A252702 A033135 A127053 Adjacent sequences:  A003948 A003949 A003950 * A003952 A003953 A003954 KEYWORD nonn,easy AUTHOR EXTENSIONS Edited by N. J. A. Sloane, Dec 04 2009 STATUS approved

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Last modified October 16 03:37 EDT 2019. Contains 328040 sequences. (Running on oeis4.)