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A169250 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

%I A169250 #12 Jul 16 2025 14:02:38
%S A169250 1,45,1980,87120,3833280,168664320,7421230080,326534123520,
%T A169250 14367501434880,632170063134720,27815482777927680,1223881242228817920,
%U A169250 53850774658067988480,2369434084954991493120,104255099738019625697280
%N A169250 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
%C A169250 The initial terms coincide with those of A170764, although the two sequences are eventually different.
%C A169250 First disagreement at index 28: a(28) = 10627589692020321608327626358553423198950521890, A170764(28) = 10627589692020321608327626358553423198950522880. - _Klaus Brockhaus_, May 24 2011
%C A169250 Computed with Magma using commands similar to those used to compute A154638.
%H A169250 <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, -946).
%F A169250 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)/(946*t^28 - 43*t^27 - 43*t^26 - 43*t^25 - 43*t^24 - 43*t^23 - 43*t^22 - 43*t^21 - 43*t^20 - 43*t^19 - 43*t^18 - 43*t^17 - 43*t^16 - 43*t^15 - 43*t^14 - 43*t^13 - 43*t^12 - 43*t^11 - 43*t^10 - 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).
%t A169250 coxG[{28,946,-43}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 16 2025 *)
%Y A169250 Cf. A170764 (G.f.: (1+x)/(1-44*x)).
%K A169250 nonn
%O A169250 0,2
%A A169250 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009