0,2

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.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 313

Index entries for sequences related to trees

a(n) = Sum_{ 0<=k<=n } A029653(n, k)*x^k for x = 10 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 10 2005

G.f.: (1+x)/(1-11x). The Hankel transform of this sequence is [1,-12,0,0,0,0,0,0,0,...]. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 21 2007

a(0) = 1; for n>0, a(n) = 12*11^(n-1). [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Dec 05 2009]

For n=1, a(1)=12; n=2, a(2)=12*11=132; n=3, a(3)=12*11^2=1452 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Dec 05 2009]

k := 12; if n = 0 then 1 else k*(k-1)^(n-1); fi;

Sequence in context: A010580 A010577 A063813 this_sequence A120673 A120674 A016123

Adjacent sequences: A003951 A003952 A003953 this_sequence A003955 A003956 A003957

nonn,new

N. J. A. Sloane (njas(AT)research.att.com).

Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 04 2009.