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A170371 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

%I A170371 #8 Nov 05 2021 13:56:31
%S A170371 1,26,650,16250,406250,10156250,253906250,6347656250,158691406250,
%T A170371 3967285156250,99182128906250,2479553222656250,61988830566406250,
%U A170371 1549720764160156250,38743019104003906250,968575477600097656250
%N A170371 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
%C A170371 The initial terms coincide with those of A170745, although the two sequences are eventually different.
%C A170371 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170371 <a href="/index/Rec#order_43">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, -300).
%F A170371 G.f. (t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 +
%F A170371 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A170371 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 A170371 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 A170371 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 A170371 + 2*t^2 + 2*t + 1)/(300*t^43 - 24*t^42 - 24*t^41 - 24*t^40 - 24*t^39 -
%F A170371 24*t^38 - 24*t^37 - 24*t^36 - 24*t^35 - 24*t^34 - 24*t^33 - 24*t^32 -
%F A170371 24*t^31 - 24*t^30 - 24*t^29 - 24*t^28 - 24*t^27 - 24*t^26 - 24*t^25 -
%F A170371 24*t^24 - 24*t^23 - 24*t^22 - 24*t^21 - 24*t^20 - 24*t^19 - 24*t^18 -
%F A170371 24*t^17 - 24*t^16 - 24*t^15 - 24*t^14 - 24*t^13 - 24*t^12 - 24*t^11 -
%F A170371 24*t^10 - 24*t^9 - 24*t^8 - 24*t^7 - 24*t^6 - 24*t^5 - 24*t^4 - 24*t^3 -
%F A170371 24*t^2 - 24*t + 1)
%t A170371 coxG[{43,300,-24}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 05 2021 *)
%K A170371 nonn
%O A170371 0,2
%A A170371 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009