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A169391 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169391 #16 Oct 11 2024 23:02:51
%S A169391 1,42,1722,70602,2894682,118681962,4865960442,199504378122,
%T A169391 8179679503002,335366859623082,13750041244546362,563751691026400842,
%U A169391 23113819332082434522,947666592615379815402,38854330297230572431482
%N A169391 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169391 The initial terms coincide with those of A170761, although the two sequences are eventually different.
%C A169391 First disagreement at index 31: a(31) = 101569892310159859486447627187803888815732132961581, A170761(31) = 101569892310159859486447627187803888815732132962442. - _Klaus Brockhaus_, Jun 17 2011
%C A169391 Computed with Magma using commands similar to those used to compute A154638.
%H A169391 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, -820).
%F A169391 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)/(820*t^31 - 40*t^30 - 40*t^29 - 40*t^28 - 40*t^27 - 40*t^26 - 40*t^25 - 40*t^24 - 40*t^23 - 40*t^22 - 40*t^21 - 40*t^20 - 40*t^19 - 40*t^18 - 40*t^17 - 40*t^16 - 40*t^15 - 40*t^14 - 40*t^13 - 40*t^12 - 40*t^11 - 40*t^10 - 40*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1).
%t A169391 coxG[{31,820,-40}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 30 2018 *)
%Y A169391 Cf. A170761 (G.f.: (1+x)/(1-41*x)).
%K A169391 nonn
%O A169391 0,2
%A A169391 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009