A073913 Number of staircase polygons on the square lattice with perimeter 2n and one (possibly rotated) staircase polygonal hole.
1, 12, 94, 604, 3461, 18412, 93016, 452500, 2139230, 9890404, 44921002, 201099320, 889594210, 3896177956, 16920602244, 72954802376, 312595497011, 1332153819572, 5650155211024, 23864065957572, 100418115489408
Offset: 8
Keywords
Links
- Iwan Jensen, Table of n, a(n) for n = 8..125 [Data from web page]
- Iwan Jensen, Polygon enumerations.
- Iwan Jensen and Andrew Rechnitzer, The exact perimeter generating function for a model of punctured staircase polygons, J. Phys. A: Math. Theor. 41 (2008) 215002, Table 1.
Formula
G.f.: -(1/4)*(f1(x)-f2(x)+f3(x)-f4(x)) where f1(x) = (1-8*x+16*x^2-4*x^3)/(1-4*x), f2(x) = (1-6*x+6*x^2)/sqrt(1-4*x), f3(x) = (1/sqrt(2))*(sqrt(2+sqrt(3+4*x))*(3-8*x+2*x^2-sqrt(3+4*x)*(1-2*x)))/(1-4*x)^(3/4), f4(x) = (1/sqrt(2))*((3-8*x+2*x^2+sqrt(3+4*x)*(1-2*x)))/(1-4*x)^(1/4)/sqrt(2+sqrt(3+4*x)) [from Jensen and Rechnitzer, 2008]. - Sean A. Irvine, Dec 27 2024
Extensions
Offset corrected by Sean A. Irvine, Dec 27 2024
Comments