cp's OEIS Frontend

A170563 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.

%I A170563 #8 Apr 23 2024 11:06:14
%S A170563 1,26,650,16250,406250,10156250,253906250,6347656250,158691406250,
%T A170563 3967285156250,99182128906250,2479553222656250,61988830566406250,
%U A170563 1549720764160156250,38743019104003906250,968575477600097656250
%N A170563 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
%C A170563 The initial terms coincide with those of A170745, although the two sequences are eventually different.
%C A170563 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170563 <a href="/index/Rec#order_47">Index entries for linear recurrences with constant coefficients</a>, signature (24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, -300).
%F A170563 G.f. (t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 +
%F A170563 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 +
%F A170563 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 A170563 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 A170563 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 A170563 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(300*t^47 -
%F A170563 24*t^46 - 24*t^45 - 24*t^44 - 24*t^43 - 24*t^42 - 24*t^41 - 24*t^40 -
%F A170563 24*t^39 - 24*t^38 - 24*t^37 - 24*t^36 - 24*t^35 - 24*t^34 - 24*t^33 -
%F A170563 24*t^32 - 24*t^31 - 24*t^30 - 24*t^29 - 24*t^28 - 24*t^27 - 24*t^26 -
%F A170563 24*t^25 - 24*t^24 - 24*t^23 - 24*t^22 - 24*t^21 - 24*t^20 - 24*t^19 -
%F A170563 24*t^18 - 24*t^17 - 24*t^16 - 24*t^15 - 24*t^14 - 24*t^13 - 24*t^12 -
%F A170563 24*t^11 - 24*t^10 - 24*t^9 - 24*t^8 - 24*t^7 - 24*t^6 - 24*t^5 - 24*t^4
%F A170563 - 24*t^3 - 24*t^2 - 24*t + 1)
%t A170563 coxG[{47,300,-24}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 23 2024 *)
%K A170563 nonn
%O A170563 0,2
%A A170563 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009