cp's OEIS Frontend

A168953 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.

%I A168953 #10 May 20 2021 17:13:37
%S A168953 1,36,1260,44100,1543500,54022500,1890787500,66177562500,
%T A168953 2316214687500,81067514062500,2837362992187500,99307704726562500,
%U A168953 3475769665429687500,121651938290039062500,4257817840151367187500,149023624405297851562500
%N A168953 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
%C A168953 The initial terms coincide with those of A170755, although the two sequences are eventually different.
%C A168953 First disagreement at index 22: a(22) = 9588075212000953794479370117186870, A170755(22) = 9588075212000953794479370117187500. - Klaus Brockhaus, Apr 10 2011
%C A168953 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168953 <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, -595).
%F A168953 G.f.: (t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(595*t^22 - 34*t^21 - 34*t^20 - 34*t^19 - 34*t^18 - 34*t^17 - 34*t^16 - 34*t^15 - 34*t^14 - 34*t^13 - 34*t^12 - 34*t^11 - 34*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).
%t A168953 coxG[{22,595,-34}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 20 2021 *)
%Y A168953 Cf. A170755 (G.f.: (1+x)/(1-35*x)).
%K A168953 nonn
%O A168953 0,2
%A A168953 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009