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 A161699 #28 Sep 08 2022 08:45:45
%S A161699 1,6,20,50,104,190,315,484,699,958,1255,1580,1919,2254,2565,2832,3037,
%T A161699 3166,3210,3166,3037,2832,2565,2254,1919,1580,1255,958,699,484,315,
%U A161699 190,104,50,20,6,1
%N A161699 Number of reduced words of length n in the Weyl group B_6.
%C A161699 Computed with MAGMA using commands similar to those used to compute A161409.
%D A161699 J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
%D A161699 N. Bourbaki, Groupes et algèbres de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)
%H A161699 G. C. Greubel, <a href="/A161699/b161699.txt">Table of n, a(n) for n = 0..36</a>
%F A161699 G.f. for B_m is the polynomial Product_{k=1..m}(1-x^(2k))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A128084.
%p A161699 seq(coeff(series(mul((1-x^(2*k))/(1-x),k=1..6),x,n+1), x, n), n = 0 .. 36); # _Muniru A Asiru_, Oct 25 2018
%t A161699 CoefficientList[Series[(1 - x^2) (1 - x^4) (1 - x^6) (1 - x^8) (1 - x^10) (1 - x^12) / (1 - x)^6, {x, 0, 50}], x] (* _Vincenzo Librandi_, Aug 22 2016 *)
%o A161699 (PARI) t='t+O('t^40); Vec(prod(k=1,6,1-t^(2*k))/(1-t)^6) \\ _G. C. Greubel_, Oct 25 2018
%o A161699 (Magma) m:=40; R<t>:=PowerSeriesRing(Integers(), m); Coefficients(R!((&*[1-t^(2*k): k in [1..6]])/(1-t)^6)); // _G. C. Greubel_, Oct 25 2018
%Y A161699 The growth series for the finite Coxeter (or Weyl) groups B_2 through B_12 are A161696-A161699, A161716, A161717, A161733, A161755, A161776, A161858. These are all rows of A128084. The growth series for the affine Coxeter (or Weyl) groups B_2 through B_12 are A008576, A008137, A267167-A267175.
%K A161699 nonn,fini,full
%O A161699 0,2
%A A161699 _John Cannon_ and _N. J. A. Sloane_, Nov 30 2009