cp's OEIS Frontend

A169565 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A169565 #8 Nov 03 2020 20:36:14
%S A169565 1,24,552,12696,292008,6716184,154472232,3552861336,81715810728,
%T A169565 1879463646744,43227663875112,994236269127576,22867434189934248,
%U A169565 525950986368487704,12096872686475217192,278228071788929995416
%N A169565 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A169565 The initial terms coincide with those of A170743, although the two sequences are eventually different.
%C A169565 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169565 <a href="/index/Rec#order_35">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, -253).
%F A169565 G.f. (t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A169565 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +
%F A169565 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +
%F A169565 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3
%F A169565 + 2*t^2 + 2*t + 1)/(253*t^35 - 22*t^34 - 22*t^33 - 22*t^32 - 22*t^31 -
%F A169565 22*t^30 - 22*t^29 - 22*t^28 - 22*t^27 - 22*t^26 - 22*t^25 - 22*t^24 -
%F A169565 22*t^23 - 22*t^22 - 22*t^21 - 22*t^20 - 22*t^19 - 22*t^18 - 22*t^17 -
%F A169565 22*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 -
%F A169565 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 -
%F A169565 22*t + 1)
%t A169565 coxG[{35,253,-22}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 03 2020 *)
%K A169565 nonn
%O A169565 0,2
%A A169565 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009