cp's OEIS Frontend

A170243 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.

%I A170243 #8 Jul 12 2019 13:40:57
%S A170243 1,42,1722,70602,2894682,118681962,4865960442,199504378122,
%T A170243 8179679503002,335366859623082,13750041244546362,563751691026400842,
%U A170243 23113819332082434522,947666592615379815402,38854330297230572431482
%N A170243 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
%C A170243 The initial terms coincide with those of A170761, although the two sequences are eventually different.
%C A170243 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170243 <a href="/index/Rec#order_40">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, -820).
%F A170243 G.f. (t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 +
%F A170243 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 +
%F A170243 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 +
%F A170243 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 +
%F A170243 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170243 1)/(820*t^40 - 40*t^39 - 40*t^38 - 40*t^37 - 40*t^36 - 40*t^35 - 40*t^34
%F A170243 - 40*t^33 - 40*t^32 - 40*t^31 - 40*t^30 - 40*t^29 - 40*t^28 - 40*t^27 -
%F A170243 40*t^26 - 40*t^25 - 40*t^24 - 40*t^23 - 40*t^22 - 40*t^21 - 40*t^20 -
%F A170243 40*t^19 - 40*t^18 - 40*t^17 - 40*t^16 - 40*t^15 - 40*t^14 - 40*t^13 -
%F A170243 40*t^12 - 40*t^11 - 40*t^10 - 40*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5
%F A170243 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1)
%t A170243 coxG[{40,820,-40}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 12 2019 *)
%K A170243 nonn
%O A170243 0,2
%A A170243 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009