cp's OEIS Frontend

A170163 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

%I A170163 #8 Oct 12 2022 16:37:27
%S A170163 1,10,90,810,7290,65610,590490,5314410,47829690,430467210,3874204890,
%T A170163 34867844010,313810596090,2824295364810,25418658283290,
%U A170163 228767924549610,2058911320946490,18530201888518410,166771816996665690
%N A170163 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
%C A170163 The initial terms coincide with those of A003952, although the two sequences are eventually different.
%C A170163 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170163 <a href="/index/Rec#order_39">Index entries for linear recurrences with constant coefficients</a>, signature (8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -36).
%F A170163 G.f. (t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170163 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 +
%F A170163 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 +
%F A170163 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 +
%F A170163 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^39 -
%F A170163 8*t^38 - 8*t^37 - 8*t^36 - 8*t^35 - 8*t^34 - 8*t^33 - 8*t^32 - 8*t^31 -
%F A170163 8*t^30 - 8*t^29 - 8*t^28 - 8*t^27 - 8*t^26 - 8*t^25 - 8*t^24 - 8*t^23 -
%F A170163 8*t^22 - 8*t^21 - 8*t^20 - 8*t^19 - 8*t^18 - 8*t^17 - 8*t^16 - 8*t^15 -
%F A170163 8*t^14 - 8*t^13 - 8*t^12 - 8*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 -
%F A170163 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1)
%t A170163 coxG[{39,36,-8}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 12 2022 *)
%K A170163 nonn
%O A170163 0,2
%A A170163 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009