OFFSET
0,2
COMMENTS
Characterized as the signed permutations avoiding the list of patterns: '((1 -2) (-2 -1 -3) (3 -2 1) (3 -2 -1) (-3 2 -1) (-3 -2 1) (-3 -2 -1)(-2 -4 3 1) (3 4 1 2) (3 4 -1 2) (-3 4 1 2) (-3 4 -1 2)(-3 -4 -1 -2) (4 -1 3 -2) (4 2 3 1) (4 2 3 -1) (-4 2 3 1))
LINKS
S. C. Billey, Pattern Avoidance and Rational Smoothness of Schubert varieties, Advances in Math, vol. 139 (1998) pp. 141-156.
E. Richmond and W. Slofstra, Staircase diagrams and enumeration of smooth Schubert varieties, arXiv:1510.06060 [math.CO], 2015; J. Combin. Ser. A, Vol 150 (2017) pp. 328-376.
FORMULA
G.f.: ((1-7*x+15*x^2-11*x^3-2*x^4+5*x^5)+(x-x^2-x^3+3*x^4-x^5)*sqrt(1-4*x))/((1-x)^2*(1-6*x+8*x^2-4*x^3)). - Edward Richmond, Apr 06 2021
PROG
(PARI) seq(n)={Vec(((1-7*x+15*x^2-11*x^3-2*x^4+5*x^5)+(x-x^2-x^3+3*x^4-x^5)*sqrt(1-4*x + O(x^n)))/((1-x)^2*(1-6*x+8*x^2-4*x^3)))} \\ Andrew Howroyd, Apr 06 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Sara Billey, Apr 02 2013
EXTENSIONS
a(0)=1 prepended and a(11) and beyond added by Edward Richmond, Apr 05 2021
STATUS
approved