0,2

Coordination sequence for infinite tree with valency 10.

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 311

Index entries for sequences related to trees

a(n)=(10*9^n-0^n)/9. Binomial transform is A000042. - Paul Barry (pbarry(AT)wit.ie), Jan 29 2004

G.f.: (1+x)/(1-9x). - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 31 2004

a(n) = Sum_{ 0<=k<=n } A029653(n, k)*x^k for x = 8 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 10 2005

The Hankel transform of this sequence is [1,-10,0,0,0,0,0,0,0,...]. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 21 2007

a(0) = 1; for n>0, a(n) = 10*9^(n-1). [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Dec 05 2009]

For n=1, a(1)=10; n=2, a(2)=10*9=90; n=3, a(3)=10*9^2=810 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Dec 05 2009]

k := 10; if n = 0 then 1 else k*(k-1)^(n-1); fi;

Sequence in context: A092420 A010579 A010576 this_sequence A033136 A061206 A137684

Adjacent sequences: A003949 A003950 A003951 this_sequence A003953 A003954 A003955

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.