cp's OEIS Frontend

A170273 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.

%I A170273 #8 Nov 22 2016 11:49:49
%S A170273 1,24,552,12696,292008,6716184,154472232,3552861336,81715810728,
%T A170273 1879463646744,43227663875112,994236269127576,22867434189934248,
%U A170273 525950986368487704,12096872686475217192,278228071788929995416
%N A170273 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
%C A170273 The initial terms coincide with those of A170743, although the two sequences are eventually different.
%C A170273 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170273 <a href="/index/Rec#order_41">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, -253).
%F A170273 G.f. (t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170273 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A170273 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A170273 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A170273 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170273 1)/(253*t^41 - 22*t^40 - 22*t^39 - 22*t^38 - 22*t^37 - 22*t^36 - 22*t^35
%F A170273 - 22*t^34 - 22*t^33 - 22*t^32 - 22*t^31 - 22*t^30 - 22*t^29 - 22*t^28 -
%F A170273 22*t^27 - 22*t^26 - 22*t^25 - 22*t^24 - 22*t^23 - 22*t^22 - 22*t^21 -
%F A170273 22*t^20 - 22*t^19 - 22*t^18 - 22*t^17 - 22*t^16 - 22*t^15 - 22*t^14 -
%F A170273 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 -
%F A170273 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1)
%t A170273 coxG[{41,253,-22}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 21 2016 *)
%K A170273 nonn
%O A170273 0,2
%A A170273 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009