A364643 Number of separable elements of the Weyl group of type D_n.
1, 2, 4, 22, 102, 474, 2250, 10910, 53886, 270322, 1373970, 7061542, 36639702, 191677386, 1009942362, 5354887470, 28550730222, 152979375842, 823329316386, 4448856020534, 24126427982406, 131270003806906, 716377546590186, 3920251765198782, 21507301494123102, 118269635529457874
Offset: 0
Keywords
Links
- Christian Gaetz and Yibo Gao, Separable elements in Weyl groups, arXiv:1905.09331 [math.CO], 2019.
Crossrefs
Types A_n and B_n/C_n are counted by A006318 (large Schröder numbers).
Programs
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Mathematica
b[0] = 1 ; a[0] = 1; a[1] = 2; a[2] = 4; b[n_Integer] := b[n] = b[n - 1] + Sum[b[k]*b[n - 1 - k], {k, 0, n - 1}]; a[n_Integer] := a[n] = a[n - 1] + b[n - 2] + 2*b[n - 1] + Sum[b[k]*a[n - k - 1], {k, 0, n - 3}]; Table[a[n], {n, 0, 30}] (* Andy Huchala, Aug 01 2023 *) -
Sage
prec = 10 R.
= PowerSeriesRing(QQ,prec) f = (3 - 4*x - 5*x^2 - (1 - x)*sqrt(1 - 6*x + x^2))/(1 - x + sqrt(1 - 6*x + x^2)) list(f) # Andy Huchala, Jul 31 2023
Formula
G.f.: (3 - 4*x - 5*x^2 - (1 - x)*sqrt(1 - 6*x + x^2))/(1 - x + sqrt(1 - 6*x + x^2)).
D-finite with recurrence +2*(n+1)*a(n) +3*(-5*n+3)*a(n-1) +(18*n-43)*a(n-2) +3*(3*n-14)*a(n-3) +2*(-n+6)*a(n-4)=0. - R. J. Mathar, Mar 25 2024