cp's OEIS Frontend

A170417 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.

%I A170417 #8 Feb 03 2019 16:41:37
%S A170417 1,24,552,12696,292008,6716184,154472232,3552861336,81715810728,
%T A170417 1879463646744,43227663875112,994236269127576,22867434189934248,
%U A170417 525950986368487704,12096872686475217192,278228071788929995416
%N A170417 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
%C A170417 The initial terms coincide with those of A170743, although the two sequences are eventually different.
%C A170417 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170417 <a href="/index/Rec#order_44">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, 22, 22, 22, 22, 22, -253).
%F A170417 G.f. (t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 +
%F A170417 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170417 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170417 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170417 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4
%F A170417 + 2*t^3 + 2*t^2 + 2*t + 1)/(253*t^44 - 22*t^43 - 22*t^42 - 22*t^41 -
%F A170417 22*t^40 - 22*t^39 - 22*t^38 - 22*t^37 - 22*t^36 - 22*t^35 - 22*t^34 -
%F A170417 22*t^33 - 22*t^32 - 22*t^31 - 22*t^30 - 22*t^29 - 22*t^28 - 22*t^27 -
%F A170417 22*t^26 - 22*t^25 - 22*t^24 - 22*t^23 - 22*t^22 - 22*t^21 - 22*t^20 -
%F A170417 22*t^19 - 22*t^18 - 22*t^17 - 22*t^16 - 22*t^15 - 22*t^14 - 22*t^13 -
%F A170417 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5
%F A170417 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1)
%t A170417 coxG[{44,253,-22}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 03 2019 *)
%K A170417 nonn
%O A170417 0,2
%A A170417 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009