cp's OEIS Frontend

A170034 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170034 #8 Jul 21 2021 19:11:13
%S A170034 1,25,600,14400,345600,8294400,199065600,4777574400,114661785600,
%T A170034 2751882854400,66045188505600,1585084524134400,38042028579225600,
%U A170034 913008685901414400,21912208461633945600,525893003079214694400
%N A170034 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170034 The initial terms coincide with those of A170744, although the two sequences are eventually different.
%C A170034 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170034 <a href="/index/Rec#order_36">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, 23, 23, -276).
%F A170034 G.f. (t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170034 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170034 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170034 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
%F A170034 + 2*t^3 + 2*t^2 + 2*t + 1)/(276*t^36 - 23*t^35 - 23*t^34 - 23*t^33 -
%F A170034 23*t^32 - 23*t^31 - 23*t^30 - 23*t^29 - 23*t^28 - 23*t^27 - 23*t^26 -
%F A170034 23*t^25 - 23*t^24 - 23*t^23 - 23*t^22 - 23*t^21 - 23*t^20 - 23*t^19 -
%F A170034 23*t^18 - 23*t^17 - 23*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 -
%F A170034 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4
%F A170034 - 23*t^3 - 23*t^2 - 23*t + 1)
%t A170034 coxG[{36,276,-23}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 21 2021 *)
%K A170034 nonn
%O A170034 0,2
%A A170034 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009