cp's OEIS Frontend

A170147 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.

%I A170147 #8 May 27 2024 18:18:07
%S A170147 1,42,1722,70602,2894682,118681962,4865960442,199504378122,
%T A170147 8179679503002,335366859623082,13750041244546362,563751691026400842,
%U A170147 23113819332082434522,947666592615379815402,38854330297230572431482
%N A170147 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
%C A170147 The initial terms coincide with those of A170761, although the two sequences are eventually different.
%C A170147 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170147 <a href="/index/Rec#order_38">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, -820).
%F A170147 G.f. (t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 +
%F A170147 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 +
%F A170147 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 +
%F A170147 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 +
%F A170147 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(820*t^38 - 40*t^37 -
%F A170147 40*t^36 - 40*t^35 - 40*t^34 - 40*t^33 - 40*t^32 - 40*t^31 - 40*t^30 -
%F A170147 40*t^29 - 40*t^28 - 40*t^27 - 40*t^26 - 40*t^25 - 40*t^24 - 40*t^23 -
%F A170147 40*t^22 - 40*t^21 - 40*t^20 - 40*t^19 - 40*t^18 - 40*t^17 - 40*t^16 -
%F A170147 40*t^15 - 40*t^14 - 40*t^13 - 40*t^12 - 40*t^11 - 40*t^10 - 40*t^9 -
%F A170147 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 A170147 coxG[{38, 820, -40}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 27 2024 *)
%K A170147 nonn
%O A170147 0,2
%A A170147 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009