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

8,2

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.

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

Crossrefs

Cf. A057410, A057414.

Sequence in context: A044644 A173348 A294449 * A057410 A045894 A045829

Adjacent sequences: A073910 A073911 A073912 * A073914 A073915 A073916

Keyword

nonn

Author

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

Extensions

Offset corrected by Sean A. Irvine, Dec 27 2024

Status

approved