cp's OEIS Frontend

A169535 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.

%I A169535 #8 Jun 25 2018 12:04:34
%S A169535 1,42,1722,70602,2894682,118681962,4865960442,199504378122,
%T A169535 8179679503002,335366859623082,13750041244546362,563751691026400842,
%U A169535 23113819332082434522,947666592615379815402,38854330297230572431482
%N A169535 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
%C A169535 The initial terms coincide with those of A170761, although the two sequences are eventually different.
%C A169535 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169535 <a href="/index/Rec#order_34">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, 40, 40, 40, -820).
%F A169535 G.f. (t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A169535 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A169535 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A169535 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 +
%F A169535 2*t + 1)/(820*t^34 - 40*t^33 - 40*t^32 - 40*t^31 - 40*t^30 - 40*t^29 -
%F A169535 40*t^28 - 40*t^27 - 40*t^26 - 40*t^25 - 40*t^24 - 40*t^23 - 40*t^22 -
%F A169535 40*t^21 - 40*t^20 - 40*t^19 - 40*t^18 - 40*t^17 - 40*t^16 - 40*t^15 -
%F A169535 40*t^14 - 40*t^13 - 40*t^12 - 40*t^11 - 40*t^10 - 40*t^9 - 40*t^8 -
%F A169535 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1)
%t A169535 coxG[{34,820,-40}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 25 2018 *)
%K A169535 nonn
%O A169535 0,2
%A A169535 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009