Search: id:A003954
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%I A003954
%S A003954 1,12,132,1452,15972,175692,1932612,21258732,233846052,
%T A003954 2572306572,28295372292,311249095212,3423740047332,37661140520652,
%U A003954 414272545727172,4556998002998892,50126978032987812
%N A003954 G.f.: (1+x)/(1-11*x).
%C A003954 Coordination sequence for infinite tree with valency 12.
%C A003954 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.
%H A003954 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=313">
               Encyclopedia of Combinatorial Structures 313</a>
%H A003954 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%F A003954 a(n) = Sum_{ 0<=k<=n } A029653(n, k)*x^k for x = 10 . - Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Jul 10 2005
%F A003954 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
%F A003954 a(0) = 1; for n>0, a(n) = 12*11^(n-1). [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Dec 05 2009]
%e A003954 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]
%p A003954 k := 12; if n = 0 then 1 else k*(k-1)^(n-1); fi;
%Y A003954 Sequence in context: A010580 A010577 A063813 this_sequence A120673 A120674 
               A016123
%Y A003954 Adjacent sequences: A003951 A003952 A003953 this_sequence A003955 A003956 
               A003957
%K A003954 nonn,new
%O A003954 0,2
%A A003954 N. J. A. Sloane (njas(AT)research.att.com).
%E A003954 Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 04 2009.

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