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A169373 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169373 #10 May 08 2018 00:33:56
%S A169373 1,24,552,12696,292008,6716184,154472232,3552861336,81715810728,
%T A169373 1879463646744,43227663875112,994236269127576,22867434189934248,
%U A169373 525950986368487704,12096872686475217192,278228071788929995416
%N A169373 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169373 The initial terms coincide with those of A170743, although the two sequences are eventually different.
%C A169373 First disagreement at index 31: a(31) = 1706264370987632712585349302874103923162500, A170743(31) = 1706264370987632712585349302874103923162776. - _Klaus Brockhaus_, Jun 17 2011
%C A169373 Computed with Magma using commands similar to those used to compute A154638.
%H A169373 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, -253).
%F A169373 G.f.: (t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*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)/(253*t^31 - 22*t^30 - 22*t^29 - 22*t^28 - 22*t^27 - 22*t^26 - 22*t^25 - 22*t^24 - 22*t^23 - 22*t^22 - 22*t^21 - 22*t^20 - 22*t^19 - 22*t^18 - 22*t^17 - 22*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).
%Y A169373 Cf. A170743 (G.f.: (1+x)/(1-23*x)).
%K A169373 nonn
%O A169373 0,2
%A A169373 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009