Search: id:A035610
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%I A035610
%S A035610 1,4,28,232,2092,19864,195352,1970896,20275660,211823800,
%T A035610 2240795848,23951289520,258255469816,2805534253552,30675477376432,
%U A035610 337306474674592,3727578443380492,41376874025687032,461121792658583272
%N A035610 G.f.: 3/(1+2*sqrt(1-12*x)).
%C A035610 Number of walks of length 2n on the 4-regular tree beginning and ending 
               at some fixed vertex. The generating function for the corresponding 
               sequence for the m-regular tree is 2*(m-1)/(m-2+m*sqrt(1-4*(m-1)*x)). 
               When m=2 this reduces to the usual generating function for the central 
               binomial coefficients. - Paul Boddington (psb(AT)maths.warwick.ac.uk), 
               Nov 11 2003
%C A035610 Main diagonal of the array A(0,j)=A(i,0)=1 for i,j>=0 and for i,j>=1 
               A(i,j)=min{A(i,j-1)+3*A(i-1,j); 3*A(i,j-1)+A(i-1,j)} - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), Aug 05 2004
%C A035610 Hankel transform is A133461 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Dec 01 2007
%F A035610 a(n) = Sum{k, 0<=k<=n}A039599(n,k)*3^(n-k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Aug 25 2007
%F A035610 Contribution from Paul Barry (pbarry(AT)wit.ie), Sep 15 2009: (Start)
%F A035610 G.f.: 1/(1-4x*c(3x)), c(x) the g.f. of A000108;
%F A035610 G.f.: 1/(1-4x/(1-3x/(1-3x/(1-3x/(1-3x/(1-.... (continued fraction);
%F A035610 G.f.: 1/(1-4x-12x^2/(1-6x-9x^2/(1-6x-9x^2/(1-6x-9x^2/(1-... (continued 
               fraction).
%F A035610 Integral representation: a(n)=(2/pi)*Int(x^n*sqrt(x(12-x))/(16-x),x,0,
               12). (End)
%e A035610 a(2)=28 because there are 4*4=16 walks whose second step is to return 
               to the starting vertex and 4*3=12 walks whose second step is to move 
               away from the starting vertex.
%t A035610 CoefficientList[ Series[3/(1 + 2Sqrt[1 - 12x]), {x, 0, 19}], x] (from 
               Robert G. Wilson v Nov 12 2003)
%Y A035610 Cf. A089022.
%Y A035610 Sequence in context: A121203 A152599 A089023 this_sequence A046904 A030444 
               A093877
%Y A035610 Adjacent sequences: A035607 A035608 A035609 this_sequence A035611 A035612 
               A035613
%K A035610 nonn
%O A035610 0,2
%A A035610 N. J. A. Sloane (njas(AT)research.att.com).

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