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A170323 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%I A170323 #8 Mar 29 2023 13:07:31
%S A170323 1,26,650,16250,406250,10156250,253906250,6347656250,158691406250,
%T A170323 3967285156250,99182128906250,2479553222656250,61988830566406250,
%U A170323 1549720764160156250,38743019104003906250,968575477600097656250
%N A170323 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
%C A170323 The initial terms coincide with those of A170745, although the two sequences are eventually different.
%C A170323 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170323 <a href="/index/Rec#order_42">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, -300).
%F A170323 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 A170323 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 A170323 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 A170323 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 A170323 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 A170323 2*t + 1)/(300*t^42 - 24*t^41 - 24*t^40 - 24*t^39 - 24*t^38 - 24*t^37 -
%F A170323 24*t^36 - 24*t^35 - 24*t^34 - 24*t^33 - 24*t^32 - 24*t^31 - 24*t^30 -
%F A170323 24*t^29 - 24*t^28 - 24*t^27 - 24*t^26 - 24*t^25 - 24*t^24 - 24*t^23 -
%F A170323 24*t^22 - 24*t^21 - 24*t^20 - 24*t^19 - 24*t^18 - 24*t^17 - 24*t^16 -
%F A170323 24*t^15 - 24*t^14 - 24*t^13 - 24*t^12 - 24*t^11 - 24*t^10 - 24*t^9 -
%F A170323 24*t^8 - 24*t^7 - 24*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1)
%t A170323 coxG[{42,300,-24}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Mar 29 2023 *)
%K A170323 nonn
%O A170323 0,2
%A A170323 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009