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A169229 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

%I A169229 #10 May 10 2018 02:27:58
%S A169229 1,24,552,12696,292008,6716184,154472232,3552861336,81715810728,
%T A169229 1879463646744,43227663875112,994236269127576,22867434189934248,
%U A169229 525950986368487704,12096872686475217192,278228071788929995416
%N A169229 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
%C A169229 The initial terms coincide with those of A170743, although the two sequences are eventually different.
%C A169229 First disagreement at index 28: a(28) = 140237065093090549238542722353423516052, A170743(28) = 140237065093090549238542722353423516328. - _Klaus Brockhaus_, May 24 2011
%C A169229 Computed with Magma using commands similar to those used to compute A154638.
%H A169229 <a href="/index/Rec#order_28">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, -253).
%F A169229 G.f.: (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^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 A169229 Cf. A170743 (G.f.: (1+x)/(1-23*x)).
%K A169229 nonn
%O A169229 0,2
%A A169229 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009