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
G.f.: (1+x)/(1-6*x).
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<x>:=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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Dec 04 2009
STATUS
approved