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

Author

Olivier Gérard, Feb 14 2009, based on data from the web site of Iwan Jensen

Keywords

• nonn

Comments

The old entry with this A-number was a duplicate of A070844.

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.

Crossrefs

Cf. A057410, A057414.

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