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.
%I A061539 #29 Apr 06 2021 20:20:58 %S A061539 1,2,7,28,116,490,2094,9014,38988,169184,735846,3205830,13984076, %T A061539 61057108,266780436,1166320956,5101254296,22319861332,97685806958, %U A061539 427635145446,1872400460940,8199602319764,35912342632908,157304824211156,689096352589448,3018916616772272 %N A061539 Number of signed permutations in B_n which correspond to smooth Schubert varieties. These permutations avoid the following patterns: (-2 -1) (1 2 -3) (1 -2 -3) (-1 2 -3) (2 -1 -3) (-2 1 -3) (3 -2 1) (2 -4 3 1) (-2 -4 3 1) (3412) (3 4 -1 2) (-3 4 1 2) (4 1 3 -2) (4 -1 3 -2) (4 2 3 1) (4 2 3 -1) (-4 2 3 1). %C A061539 A signed permutation w corresponds to a matrix with exactly one nonzero entry in each row and column and that entry is either 1 or -1. A signed permutation avoids the pattern (1 2 -3) if no three rows and three columns gives a submatrix with diagonal entries 1 1 -1. %H A061539 Andrew Howroyd, <a href="/A061539/b061539.txt">Table of n, a(n) for n = 0..500</a> %H A061539 S. C. Billey, <a href="https://doi.org/10.1006/aima.1998.1744">Pattern Avoidance and Rational Smoothness of Schubert varieties</a>, Advances in Math, vol. 139 (1998) pp. 141-156. %H A061539 E. Richmond and W. Slofstra, <a href="https://arxiv.org/abs/1510.06060">Staircase diagrams and enumeration of smooth Schubert varieties</a>, arXiv:1510.06060 [math.CO], 2015; J. Combin. Ser. A, Vol 150 (2017) pp. 328-376. %F A061539 G.f: ((1-5*x+5*x^2)*(1-x)+(2*x-x^2)*(1-x)*sqrt(1-4*x))/(1-6*x+8*x^2-4*x^3). - _Edward Richmond_, Apr 06 2021 %e A061539 a(2) = 7 because there are 8 signed permutations of two elements and there is exactly one bad pattern of length 2. %o A061539 (PARI) seq(n)=Vec(((1-5*x+5*x^2)*(1-x)+(2*x-x^2)*(1-x)*sqrt(1-4*x + O(x^n)))/(1-6*x+8*x^2-4*x^3)) \\ _Andrew Howroyd_, Apr 06 2021 %Y A061539 Cf. A032351. %K A061539 nonn,easy %O A061539 0,2 %A A061539 _Sara Billey_, May 15 2001 %E A061539 a(0)=1 prepended and a(10)-a(25) from _Edward Richmond_, Apr 05 2021