cp's OEIS Frontend

A170339 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%I A170339 #8 Nov 22 2016 08:24:41
%S A170339 1,42,1722,70602,2894682,118681962,4865960442,199504378122,
%T A170339 8179679503002,335366859623082,13750041244546362,563751691026400842,
%U A170339 23113819332082434522,947666592615379815402,38854330297230572431482
%N A170339 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
%C A170339 The initial terms coincide with those of A170761, although the two sequences are eventually different.
%C A170339 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170339 <a href="/index/Rec#order_42">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, -820).
%F A170339 G.f. (t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170339 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A170339 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 A170339 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 A170339 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 A170339 2*t + 1)/(820*t^42 - 40*t^41 - 40*t^40 - 40*t^39 - 40*t^38 - 40*t^37 -
%F A170339 40*t^36 - 40*t^35 - 40*t^34 - 40*t^33 - 40*t^32 - 40*t^31 - 40*t^30 -
%F A170339 40*t^29 - 40*t^28 - 40*t^27 - 40*t^26 - 40*t^25 - 40*t^24 - 40*t^23 -
%F A170339 40*t^22 - 40*t^21 - 40*t^20 - 40*t^19 - 40*t^18 - 40*t^17 - 40*t^16 -
%F A170339 40*t^15 - 40*t^14 - 40*t^13 - 40*t^12 - 40*t^11 - 40*t^10 - 40*t^9 -
%F A170339 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 A170339 coxG[{42,820,-40}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 11 2016 *)
%K A170339 nonn
%O A170339 0,2
%A A170339 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009