cp's OEIS Frontend

A170099 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

%I A170099 #6 Nov 26 2016 10:10:00
%S A170099 1,42,1722,70602,2894682,118681962,4865960442,199504378122,
%T A170099 8179679503002,335366859623082,13750041244546362,563751691026400842,
%U A170099 23113819332082434522,947666592615379815402,38854330297230572431482
%N A170099 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
%C A170099 The initial terms coincide with those of A170761, although the two sequences are eventually different.
%C A170099 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170099 <a href="/index/Rec#order_37">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, -820).
%F A170099 G.f. (t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170099 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 +
%F A170099 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 +
%F A170099 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 +
%F A170099 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(820*t^37 - 40*t^36 - 40*t^35 -
%F A170099 40*t^34 - 40*t^33 - 40*t^32 - 40*t^31 - 40*t^30 - 40*t^29 - 40*t^28 -
%F A170099 40*t^27 - 40*t^26 - 40*t^25 - 40*t^24 - 40*t^23 - 40*t^22 - 40*t^21 -
%F A170099 40*t^20 - 40*t^19 - 40*t^18 - 40*t^17 - 40*t^16 - 40*t^15 - 40*t^14 -
%F A170099 40*t^13 - 40*t^12 - 40*t^11 - 40*t^10 - 40*t^9 - 40*t^8 - 40*t^7 -
%F A170099 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1)
%K A170099 nonn
%O A170099 0,2
%A A170099 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009