cp's OEIS Frontend

A170387 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

%I A170387 #8 Jul 03 2022 17:54:31
%S A170387 1,42,1722,70602,2894682,118681962,4865960442,199504378122,
%T A170387 8179679503002,335366859623082,13750041244546362,563751691026400842,
%U A170387 23113819332082434522,947666592615379815402,38854330297230572431482
%N A170387 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
%C A170387 The initial terms coincide with those of A170761, although the two sequences are eventually different.
%C A170387 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170387 <a href="/index/Rec#order_43">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, 40, 40, 40, 40, 40, 40, 40, 40, 40, -820).
%F A170387 G.f. (t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 +
%F A170387 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A170387 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +
%F A170387 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +
%F A170387 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
%F A170387 + 2*t^2 + 2*t + 1)/(820*t^43 - 40*t^42 - 40*t^41 - 40*t^40 - 40*t^39 -
%F A170387 40*t^38 - 40*t^37 - 40*t^36 - 40*t^35 - 40*t^34 - 40*t^33 - 40*t^32 -
%F A170387 40*t^31 - 40*t^30 - 40*t^29 - 40*t^28 - 40*t^27 - 40*t^26 - 40*t^25 -
%F A170387 40*t^24 - 40*t^23 - 40*t^22 - 40*t^21 - 40*t^20 - 40*t^19 - 40*t^18 -
%F A170387 40*t^17 - 40*t^16 - 40*t^15 - 40*t^14 - 40*t^13 - 40*t^12 - 40*t^11 -
%F A170387 40*t^10 - 40*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 -
%F A170387 40*t^2 - 40*t + 1)
%t A170387 coxG[{43,820,-40}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 03 2022 *)
%K A170387 nonn
%O A170387 0,2
%A A170387 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009