cp's OEIS Frontend

A170321 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%I A170321 #6 Nov 22 2016 08:13:09
%S A170321 1,24,552,12696,292008,6716184,154472232,3552861336,81715810728,
%T A170321 1879463646744,43227663875112,994236269127576,22867434189934248,
%U A170321 525950986368487704,12096872686475217192,278228071788929995416
%N A170321 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
%C A170321 The initial terms coincide with those of A170743, although the two sequences are eventually different.
%C A170321 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170321 <a href="/index/Rec#order_42">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, -253).
%F A170321 G.f. (t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
%F A170321 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A170321 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A170321 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A170321 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 +
%F A170321 2*t + 1)/(253*t^42 - 22*t^41 - 22*t^40 - 22*t^39 - 22*t^38 - 22*t^37 -
%F A170321 22*t^36 - 22*t^35 - 22*t^34 - 22*t^33 - 22*t^32 - 22*t^31 - 22*t^30 -
%F A170321 22*t^29 - 22*t^28 - 22*t^27 - 22*t^26 - 22*t^25 - 22*t^24 - 22*t^23 -
%F A170321 22*t^22 - 22*t^21 - 22*t^20 - 22*t^19 - 22*t^18 - 22*t^17 - 22*t^16 -
%F A170321 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 -
%F A170321 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1)
%K A170321 nonn
%O A170321 0,2
%A A170321 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009