Search: id:A003952
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%I A003952
%S A003952 1,10,90,810,7290,65610,590490,5314410,47829690,430467210,
%T A003952 3874204890,34867844010,313810596090,2824295364810,25418658283290,
%U A003952 228767924549610,2058911320946490,18530201888518410
%N A003952 G.f.: (1+x)/(1-9*x).
%C A003952 Coordination sequence for infinite tree with valency 10.
%C A003952 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 A003952 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=311">
               Encyclopedia of Combinatorial Structures 311</a>
%H A003952 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%F A003952 a(n)=(10*9^n-0^n)/9. Binomial transform is A000042. - Paul Barry (pbarry(AT)wit.ie), 
               Jan 29 2004
%F A003952 G.f.: (1+x)/(1-9x). - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 
               31 2004
%F A003952 a(n) = Sum_{ 0<=k<=n } A029653(n, k)*x^k for x = 8 . - Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Jul 10 2005
%F A003952 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
%F A003952 a(0) = 1; for n>0, a(n) = 10*9^(n-1). [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Dec 05 2009]
%e A003952 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]
%p A003952 k := 10; if n = 0 then 1 else k*(k-1)^(n-1); fi;
%Y A003952 Sequence in context: A092420 A010579 A010576 this_sequence A033136 A061206 
               A137684
%Y A003952 Adjacent sequences: A003949 A003950 A003951 this_sequence A003953 A003954 
               A003955
%K A003952 nonn,new
%O A003952 0,2
%A A003952 N. J. A. Sloane (njas(AT)research.att.com).
%E A003952 Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 04 2009.

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