cp's OEIS Frontend

A169477 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.

%I A169477 #8 Nov 26 2016 07:24:27
%S A169477 1,32,992,30752,953312,29552672,916132832,28400117792,880403651552,
%T A169477 27292513198112,846067909141472,26228105183385632,813071260684954592,
%U A169477 25205209081233592352,781361481518241362912,24222205927065482250272
%N A169477 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
%C A169477 The initial terms coincide with those of A170751, although the two sequences are eventually different.
%C A169477 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169477 <a href="/index/Rec#order_33">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, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, -465).
%F A169477 G.f. (t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A169477 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A169477 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A169477 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 +
%F A169477 1)/(465*t^33 - 30*t^32 - 30*t^31 - 30*t^30 - 30*t^29 - 30*t^28 - 30*t^27
%F A169477 - 30*t^26 - 30*t^25 - 30*t^24 - 30*t^23 - 30*t^22 - 30*t^21 - 30*t^20 -
%F A169477 30*t^19 - 30*t^18 - 30*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 -
%F A169477 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5
%F A169477 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1)
%t A169477 With[{num=Total[2t^Range[32]]+t^33+1,den=Total[-30 t^Range[32]]+465t^33+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, May 16 2013 *)
%K A169477 nonn
%O A169477 0,2
%A A169477 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009