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A116868
Triangle of numbers, called Y(1,3), related to generalized Catalan numbers A064063(n) = C(3;n).
3
1, 3, 4, 9, 21, 25, 27, 90, 165, 190, 81, 351, 846, 1416, 1606, 243, 1296, 3834, 8082, 12900, 14506, 729, 4617, 16119, 40365, 79065, 122583, 137089, 2187, 16038, 64395, 185490, 422685, 790434, 1201701, 1338790
OFFSET
0,2
COMMENTS
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.
The main diagonal (M=1) gives the generalized Catalan sequence C(3;n+1):= A064063(n+1).
LINKS
B. Derrida, E. Domany and D. Mukamel, An exact solution of a one-dimensional asymmetric exclusion model with open boundaries, J. Stat. Phys. 69, 1992, 667-687; eqs. (20), (21), p. 672.
Wolfdieter Lang, First 10 rows.
FORMULA
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).
EXAMPLE
Triangle begins:
1;
3, 4;
9, 21, 25;
27, 90, 165, 190;
81, 351, 846, 1416, 1606;
...
CROSSREFS
Row sums give A116862.
Sequence in context: A324764 A092763 A232955 * A049976 A032789 A299123
KEYWORD
nonn,easy,tabl
AUTHOR
Wolfdieter Lang, Mar 24 2006
STATUS
approved