Duchi, Enrica; Frosini, Andrea; Pinzani, Renzo; Rinaldi, Simone A note on rational succession rules. (English) Zbl 1013.05007 J. Integer Seq. 6, No. 1, Art. 03.1.7, 9 p. (2003). Summary: Succession rules having a rational generating function are usually called rational succession rules. In this note we discuss some problems concerning rational succession rules, and determine a simple method to pass from a rational generating function to a rational succession rule, both defining the same number sequence. Cited in 3 Documents MSC: 05A15 Exact enumeration problems, generating functions Keywords:succession rules; generating trees; rational generating functions Software:OEIS PDFBibTeX XMLCite \textit{E. Duchi} et al., J. Integer Seq. 6, No. 1, Art. 03.1.7, 9 p. (2003; Zbl 1013.05007) Full Text: EuDML EMIS Online Encyclopedia of Integer Sequences: a(n) = 3*a(n-1) - a(n-2) for n >= 2, with a(0) = a(1) = 1. NSW numbers: a(n) = 6*a(n-1) - a(n-2); also a(n)^2 - 2*b(n)^2 = -1 with b(n) = A001653(n+1). a(n) = (1 + a(n-1)*a(n-2))/a(n-3), a(0) = a(1) = a(2) = 1.