A168949 - OEIS

%I #16 Nov 25 2016 09:56:03

%S 1,32,992,30752,953312,29552672,916132832,28400117792,880403651552,

%T 27292513198112,846067909141472,26228105183385632,813071260684954592,

%U 25205209081233592352,781361481518241362912,24222205927065482250272

%N Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.

%C The initial terms coincide with those of A170751, although the two sequences are eventually different.

%C Computed with MAGMA using commands similar to those used to compute A154638.

%C From _Klaus Brockhaus_, Apr 10 2011: (Start)

%C First disagreement between this sequence and A170751 is at index 22:

%C         a(22) = 666416204588529623779853460787696,

%C   A170751(22) = 666416204588529623779853460788192. (End)

%H <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, -465).

%F 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)/(465*t^22 - 30*t^21 - 30*t^20 - 30*t^19 - 30*t^18 - 30*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).

%t With[{num=Total[2t^Range[21]]+t^22+1,den=Total[-30 t^Range[21]]+ 465t^22+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jan 06 2013 *)

%Y Cf. A170751 (G.f.: (1+x)/(1-31*x)).

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009

%E Edited by _Jon E. Schoenfield_, Apr 30 2014