cp's OEIS Frontend

A169518 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.

%I A169518 #8 Apr 05 2018 12:12:14
%S A169518 1,25,600,14400,345600,8294400,199065600,4777574400,114661785600,
%T A169518 2751882854400,66045188505600,1585084524134400,38042028579225600,
%U A169518 913008685901414400,21912208461633945600,525893003079214694400
%N A169518 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
%C A169518 The initial terms coincide with those of A170744, although the two sequences are eventually different.
%C A169518 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169518 <a href="/index/Rec#order_34">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, 23, -276).
%F A169518 G.f. (t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A169518 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A169518 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A169518 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 +
%F A169518 2*t + 1)/(276*t^34 - 23*t^33 - 23*t^32 - 23*t^31 - 23*t^30 - 23*t^29 -
%F A169518 23*t^28 - 23*t^27 - 23*t^26 - 23*t^25 - 23*t^24 - 23*t^23 - 23*t^22 -
%F A169518 23*t^21 - 23*t^20 - 23*t^19 - 23*t^18 - 23*t^17 - 23*t^16 - 23*t^15 -
%F A169518 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 -
%F A169518 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1)
%t A169518 coxG[{34,276,-23}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 05 2018 *)
%K A169518 nonn
%O A169518 0,2
%A A169518 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009