cp's OEIS Frontend

A170177 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

%I A170177 #8 Jul 06 2021 16:25:20
%S A170177 1,24,552,12696,292008,6716184,154472232,3552861336,81715810728,
%T A170177 1879463646744,43227663875112,994236269127576,22867434189934248,
%U A170177 525950986368487704,12096872686475217192,278228071788929995416
%N A170177 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
%C A170177 The initial terms coincide with those of A170743, although the two sequences are eventually different.
%C A170177 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170177 <a href="/index/Rec#order_39">Index entries for linear recurrences with constant coefficients</a>, signature (22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, -253).
%F A170177 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 A170177 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 A170177 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 A170177 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 A170177 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(253*t^39 -
%F A170177 22*t^38 - 22*t^37 - 22*t^36 - 22*t^35 - 22*t^34 - 22*t^33 - 22*t^32 -
%F A170177 22*t^31 - 22*t^30 - 22*t^29 - 22*t^28 - 22*t^27 - 22*t^26 - 22*t^25 -
%F A170177 22*t^24 - 22*t^23 - 22*t^22 - 22*t^21 - 22*t^20 - 22*t^19 - 22*t^18 -
%F A170177 22*t^17 - 22*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 -
%F A170177 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 -
%F A170177 22*t^2 - 22*t + 1)
%t A170177 coxG[{39,253,-22}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 06 2021 *)
%K A170177 nonn
%O A170177 0,2
%A A170177 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009