OFFSET
0,2
COMMENTS
This triangle Y(1,2) appears in the totally asymmetric exclusion process for the (unphysical) values alpha=1, beta=2. See the Derrida et al. refs. 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(2,n+1):=A064062(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: ((1 + 2*x*c(2*x))*(2*x*c(2*x))^m)/(2*x*(1+x)) with c(x) the o.g.f. of A000108 (Catalan).
EXAMPLE
Triangle begins:
1;
2, 3;
4, 10, 13;
8, 28, 54, 67;
16, 72, 180, 314, 381;
...
CROSSREFS
KEYWORD
AUTHOR
Wolfdieter Lang, Feb 23 2006
STATUS
approved