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A169421 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169421 #16 May 08 2018 01:10:09
%S A169421 1,24,552,12696,292008,6716184,154472232,3552861336,81715810728,
%T A169421 1879463646744,43227663875112,994236269127576,22867434189934248,
%U A169421 525950986368487704,12096872686475217192,278228071788929995416
%N A169421 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169421 The initial terms coincide with those of A170743, although the two sequences are eventually different.
%C A169421 First disagreement is at index 32, the difference is 276. - _Klaus Brockhaus_, Jun 27 2011
%C A169421 Computed with Magma using commands similar to those used to compute A154638.
%H A169421 <a href="/index/Rec#order_32">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, 22, -253).
%F A169421 G.f.: (t^32 + 2*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^32 - 22*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).
%F A169421 G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-22*sum(k=1..31, x^k)+253*x^32).
%t A169421 coxG[{32,253,-22}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Mar 27 2015 *)
%Y A169421 Cf. A170743 (G.f.: (1+x)/(1-23*x) ).
%K A169421 nonn
%O A169421 0,2
%A A169421 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009