%I A116868
%S A116868 1,3,4,9,21,25,27,90,165,190,81,351,846,1416,1606,243,1296,3834,8082,
%T A116868 12900,14506,729,4617,16119,40365,79065,122583,137089,2187,16038,64395,
%U A116868 185490,422685,790434,1201701,1338790
%N A116868 Triangle of numbers, called Y(1,3), related to generalized Catalan numbers 
               A064063(n)=:C(3;n).
%C A116868 This triangle Y(1,3) appears in the totally asymmetric exclusion process 
               for the (unphysical) values alpha=1, beta=3. See the Derrida et al. 
               reference given under A064094, where the triangle entries are called 
               Y_{N,K} for given alpha and beta.
%C A116868 The main diagonal (M=1) gives the generalized Catalan sequence C(3;n+1):= 
               A064063(n+1).
%H A116868 W. Lang: <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A116868.text">
               First 10 rows.</a>
%F A116868 G.f. m-th diagonal, m>=1:((3*x*c(3*x))^m)*(2 + 3*x*c(3*x))/(3*x*(2+x))) 
               with c(x) the o.g.f. of A000108 (Catalan).
%e A116868 [1];[3,4];[9,21,25];[27,90,165,190];[81,351,846,1416,1606];...
%Y A116868 Row sums give A116862.
%Y A116868 Sequence in context: A110810 A049978 A092763 this_sequence A049976 A032789 
               A089243
%Y A116868 Adjacent sequences: A116865 A116866 A116867 this_sequence A116869 A116870 
               A116871
%K A116868 nonn,easy,tabl
%O A116868 0,2
%A A116868 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Mar 24 
               2006