0,3

This sequence appears in the Derrida et al. 1992 reference as Z_{N}=:Y_{N}(N+1), N >=0, for alpha =2, beta = 3 (or alpha=3, beta=2). In the Derrida et al. 1993 reference the formula in eq. (39) gives Z_{N}(alpha,beta)/(alpha*beta)^N for N>=1. See also the Liggett reference, proposition 3.19, p. 269, with lambda for alpha and rho for 1-beta.

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.

B. Derrida, M. R. Evans, V. Hakim and V. Pasquier, Exact solution of a 1D asymmetric exclusion model using a matrix formulation, J. Phys. A 26, 1993, 1493-1517; eq. (39), p. 1501, also appendix A1, (A12) p. 1513.

G. Schuetz and E. Domany, Phase Transitions in an Exactly Soluble one-Dimensional Exclusion Process, J. Stat. Phys. 72 (1993) 277-295, eq. (2.18), p. 283, with eqs. (2.13)-(2.15).

T. M. Liggett, Stochastic Interacting Systems: Contact, Voter and Exclusion Processes, Springer, 1999, p. 269.

G.f.: (1+5*x+12*x^2*c(6*x))/((1+3*x)*(1+x)) with the g.f. c(x) for A000108 (Catalan numbers).

a(n)=((-1)^(n+1))*(3^n-2)+6*sum(((-1)^k)*C(n-2-k)*6^(n-2-k)*(3^(k+1)-1),k=0..n-2), with C(n):=A000108(n) (Catalan numbers), and the sum is replaced by 0 for n=0,1. Proof from the g.f. after partial fraction decomposition (W. Lang, May 05 2006).

Sequence in context: A001079 A081474 A112241 this_sequence A089914 A052142 A136729

Adjacent sequences: A116870 A116871 A116872 this_sequence A116874 A116875 A116876

nonn,easy

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Mar 24 2006