Expected number of hairpins in saturated structures

The following table is taken from Asymptotic number of hairpins of saturated RNA secondary structures, by P. Clote, E. Kranakis, D. Krizanc, submitted to Bulletin of Mathematical Biology.

Computations for table values

Values in Table 1 obtained by computations in Mathematica using Drmota's Theorem,
M.Drmota
"Systems of functional equations"
Random Structures and Algorithms
10(1-2): 103--124 (1997).

  1. drmotaTheta1P1.pdf: θ=1, p=1.
  2. drmotaTheta1P1over2.pdf: θ=1, p=1/2.
  3. drmotaTheta1P3over8.pdf: θ=1, p=3/8.
  4. drmotaTheta3P1.pdf: θ=3, p=1.
  5. drmotaTheta3P1over2.pdf: θ=3, p=1/2.
  6. drmotaTheta3P3over8.pdf: θ=3, p=3/8.
  7. drmotaTheta1P1_earlyVersion.pdf: Correct alternate computation for θ=1, p=1.