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) [1] 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) [1]+[12*11^(n-1) for n in (1..20)] # G. C. Greubel, Sep 23 2019
(GAP) Concatenation([1], List([1..20], n-> 12*11^(n-1) )); # G. C. Greubel, Sep 23 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Dec 04 2009
STATUS
approved