cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A073913 Number of staircase polygons on the square lattice with perimeter 2n and one (possibly rotated) staircase polygonal hole.

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%I A073913 #22 Jul 09 2025 03:57:07
%S A073913 1,12,94,604,3461,18412,93016,452500,2139230,9890404,44921002,
%T A073913 201099320,889594210,3896177956,16920602244,72954802376,312595497011,
%U A073913 1332153819572,5650155211024,23864065957572,100418115489408
%N A073913 Number of staircase polygons on the square lattice with perimeter 2n and one (possibly rotated) staircase polygonal hole.
%C A073913 The old entry with this A-number was a duplicate of A070844.
%H A073913 Iwan Jensen, <a href="/A073913/b073913.txt">Table of n, a(n) for n = 8..125</a> [Data from web page]
%H A073913 Iwan Jensen, <a href="http://www.ms.unimelb.edu.au/~iwan/polygons/Polygons_ser.html">Polygon enumerations.</a>
%H A073913 Iwan Jensen and Andrew Rechnitzer, <a href="http://dx.doi.org/10.1088/1751-8113/41/21/215002">The exact perimeter generating function for a model of punctured staircase polygons</a>, J. Phys. A: Math. Theor. 41 (2008) 215002, Table 1.
%F A073913 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
%Y A073913 Cf. A057410, A057414.
%K A073913 nonn
%O A073913 8,2
%A A073913 _Olivier Gérard_, Feb 14 2009, based on data from the web site of Iwan Jensen
%E A073913 Offset corrected by _Sean A. Irvine_, Dec 27 2024