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 A003949 Expansion of g.f.: (1+x)/(1-6*x). 57
 1, 7, 42, 252, 1512, 9072, 54432, 326592, 1959552, 11757312, 70543872, 423263232, 2539579392, 15237476352, 91424858112, 548549148672, 3291294892032, 19747769352192, 118486616113152, 710919696678912, 4265518180073472, 25593109080440832, 153558654482644992 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Coordination sequence for infinite tree with valency 7. For n >= 1, a(n+1) is equal to the number of functions f:{1,2,...,n+1}->{1,2,3,4,5,6,7} such that for fixed, different x_1, x_2,...,x_n in {1,2,...,n+1} and fixed y_1, y_2,...,y_n in {1,2,3,4,5,6,7} we have f(x_i)<>y_i, (i=1,2,...,n). - Milan Janjic, May 10 2007 For n >= 1, a(n) equals the numbers of words of length n-1 on alphabet {0,1,2,3,5,6} with no two adjacent letters identical. - Milan Janjic, Jan 31 2015 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 308 Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets Index entries for linear recurrences with constant coefficients, signature (6). FORMULA a(n) = Sum_{k=0..n} A029653(n, k)*x^k for x = 5. - Philippe Deléham, Jul 10 2005 a(0)=1; for n > 0, a(n) = 7*6^(n-1). - Vincenzo Librandi, Nov 18 2010 a(0)=1, a(1)=7, a(n) = 6*a(n-1). - Vincenzo Librandi, Dec 10 2012 E.g.f.: (7*exp(6*x) - 1)/6. - G. C. Greubel, Sep 24 2019 MAPLE k:=7; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # modified by G. C. Greubel, Sep 24 2019 MATHEMATICA q = 7; Join[{a = 1}, Table[If[n != 0, a = q*a - a, a = q*a], {n, 0, 25}]] (* or *) Join[{1}, 7*6^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *) CoefficientList[Series[(1+x)/(1-6*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2012 *) PROG (PARI) a(n)=if(n, 7*6^(n-1), 1) \\ Charles R Greathouse IV, Mar 22 2016 (Magma) k:=7; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 24 2019 (Magma) R:=PowerSeriesRing(Rationals(), 25); Coefficients(R!( (1+x)/(1-6*x))); // Marius A. Burtea, Jan 20 2020 (Sage) k=7; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 24 2019 (GAP) k:=7;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019 CROSSREFS Cf. A003947, A003948, A003950, A003951. Sequence in context: A170592 A170640 A170688 * A252700 A033133 A082035 Adjacent sequences: A003946 A003947 A003948 * A003950 A003951 A003952 KEYWORD nonn,easy AUTHOR EXTENSIONS Edited by N. J. A. Sloane, Dec 04 2009 STATUS approved

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Last modified February 5 03:17 EST 2023. Contains 360082 sequences. (Running on oeis4.)