cp's OEIS Frontend

A168950 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.

%I A168950 #11 Nov 25 2016 10:03:14
%S A168950 1,33,1056,33792,1081344,34603008,1107296256,35433480192,
%T A168950 1133871366144,36283883716608,1161084278931456,37154696925806592,
%U A168950 1188950301625810944,38046409652025950208,1217485108864830406656,38959523483674573012992
%N A168950 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
%C A168950 The initial terms coincide with those of A170752, although the two sequences are eventually different.
%C A168950 First disagreement at index 22: a(22) = 1338639033841010247980518584876528, A170752(22) = 1338639033841010247980518584877056. - Klaus Brockhaus, Apr 10 2011
%C A168950 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168950 <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, -496).
%F A168950 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)/(496*t^22 - 31*t^21 - 31*t^20 - 31*t^19 - 31*t^18 - 31*t^17 - 31*t^16 - 31*t^15 - 31*t^14 - 31*t^13 - 31*t^12 - 31*t^11 - 31*t^10 - 31*t^9 - 31*t^8 - 31*t^7 - 31*t^6 - 31*t^5 - 31*t^4 - 31*t^3 - 31*t^2 - 31*t + 1).
%t A168950 With[{num=Total[2t^Range[21]]+t^22+1,den=Total[-31 t^Range[21]]+ 496t^22+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Aug 21 2011 *)
%Y A168950 Cf. A170752 (G.f.: (1+x)/(1-32*x)).
%K A168950 nonn
%O A168950 0,2
%A A168950 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009