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A169295 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.

%I A169295 #12 Jul 19 2018 11:10:16
%S A169295 1,42,1722,70602,2894682,118681962,4865960442,199504378122,
%T A169295 8179679503002,335366859623082,13750041244546362,563751691026400842,
%U A169295 23113819332082434522,947666592615379815402,38854330297230572431482
%N A169295 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
%C A169295 The initial terms coincide with those of A170761, although the two sequences are eventually different.
%C A169295 First disagreement at index 29: a(29) = 60422303575347923549344216054612664375807335821, A170761(29) = 60422303575347923549344216054612664375807336682. - _Klaus Brockhaus_, Jun 03 2011
%C A169295 Computed with Magma using commands similar to those used to compute A154638.
%H A169295 <a href="/index/Rec#order_29">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, -820).
%F A169295 G.f.: (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^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 A169295 coxG[{29,820,-40}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 19 2018 *)
%Y A169295 Cf. A170761 (G.f.: (1+x)/(1-41*x)).
%K A169295 nonn
%O A169295 0,2
%A A169295 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009