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A169253 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

%I A169253 #12 May 10 2018 02:40:09
%S A169253 1,48,2256,106032,4983504,234224688,11008560336,517402335792,
%T A169253 24317909782224,1142941759764528,53718262708932816,
%U A169253 2524758347319842352,118663642324032590544,5577191189229531755568,262127985893787992511696
%N A169253 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
%C A169253 The initial terms coincide with those of A170767, although the two sequences are eventually different.
%C A169253 First disagreement at index 28: a(28) = 67279600134801960187690796333557387783807278696, A170767(28) = 67279600134801960187690796333557387783807279824. - _Klaus Brockhaus_, May 24 2011
%C A169253 Computed with Magma using commands similar to those used to compute A154638.
%H A169253 <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, -1081).
%F A169253 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)/(1081*t^28 - 46*t^27 - 46*t^26 - 46*t^25 - 46*t^24 - 46*t^23 - 46*t^22 - 46*t^21 - 46*t^20 - 46*t^19 - 46*t^18 - 46*t^17 - 46*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).
%t A169253 coxG[{28,1081,-46}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 21 2014 *)
%Y A169253 Cf. A170767 (G.f.: (1+x)/(1-47*x)).
%K A169253 nonn
%O A169253 0,2
%A A169253 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009