cp's OEIS Frontend

A169470 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.

%I A169470 #8 Nov 26 2016 07:22:32
%S A169470 1,25,600,14400,345600,8294400,199065600,4777574400,114661785600,
%T A169470 2751882854400,66045188505600,1585084524134400,38042028579225600,
%U A169470 913008685901414400,21912208461633945600,525893003079214694400
%N A169470 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
%C A169470 The initial terms coincide with those of A170744, although the two sequences are eventually different.
%C A169470 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169470 <a href="/index/Rec#order_33">Index entries for linear recurrences with constant coefficients</a>, signature (23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, -276).
%F A169470 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 A169470 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 A169470 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 A169470 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 A169470 1)/(276*t^33 - 23*t^32 - 23*t^31 - 23*t^30 - 23*t^29 - 23*t^28 - 23*t^27
%F A169470 - 23*t^26 - 23*t^25 - 23*t^24 - 23*t^23 - 23*t^22 - 23*t^21 - 23*t^20 -
%F A169470 23*t^19 - 23*t^18 - 23*t^17 - 23*t^16 - 23*t^15 - 23*t^14 - 23*t^13 -
%F A169470 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5
%F A169470 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1)
%t A169470 With[{num=Total[2t^Range[32]]+t^33+1,den=Total[-23 t^Range[32]]+ 276t^33+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jan 28 2013 *)
%K A169470 nonn
%O A169470 0,2
%A A169470 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009