cp's OEIS Frontend

A170291 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.

%I A170291 #8 Nov 22 2016 12:00:50
%S A170291 1,42,1722,70602,2894682,118681962,4865960442,199504378122,
%T A170291 8179679503002,335366859623082,13750041244546362,563751691026400842,
%U A170291 23113819332082434522,947666592615379815402,38854330297230572431482
%N A170291 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
%C A170291 The initial terms coincide with those of A170761, although the two sequences are eventually different.
%C A170291 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170291 <a href="/index/Rec#order_41">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, -820).
%F A170291 G.f. (t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170291 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A170291 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A170291 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A170291 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 +
%F A170291 1)/(820*t^41 - 40*t^40 - 40*t^39 - 40*t^38 - 40*t^37 - 40*t^36 - 40*t^35
%F A170291 - 40*t^34 - 40*t^33 - 40*t^32 - 40*t^31 - 40*t^30 - 40*t^29 - 40*t^28 -
%F A170291 40*t^27 - 40*t^26 - 40*t^25 - 40*t^24 - 40*t^23 - 40*t^22 - 40*t^21 -
%F A170291 40*t^20 - 40*t^19 - 40*t^18 - 40*t^17 - 40*t^16 - 40*t^15 - 40*t^14 -
%F A170291 40*t^13 - 40*t^12 - 40*t^11 - 40*t^10 - 40*t^9 - 40*t^8 - 40*t^7 -
%F A170291 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1)
%t A170291 coxG[{41,820,-40}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Dec 19 2014 *)
%K A170291 nonn
%O A170291 0,2
%A A170291 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009