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A170608 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.

%I A170608 #8 Aug 25 2019 11:30:49
%S A170608 1,23,506,11132,244904,5387888,118533536,2607737792,57370231424,
%T A170608 1262145091328,27767192009216,610878224202752,13439320932460544,
%U A170608 295665060514131968,6504631331310903296,143101889288839872512
%N A170608 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
%C A170608 The initial terms coincide with those of A170742, although the two sequences are eventually different.
%C A170608 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170608 <a href="/index/Rec#order_48">Index entries for linear recurrences with constant coefficients</a>, signature (21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -231).
%F A170608 G.f. (t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 +
%F A170608 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 +
%F A170608 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 +
%F A170608 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 +
%F A170608 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 +
%F A170608 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170608 1)/(231*t^48 - 21*t^47 - 21*t^46 - 21*t^45 - 21*t^44 - 21*t^43 - 21*t^42
%F A170608 - 21*t^41 - 21*t^40 - 21*t^39 - 21*t^38 - 21*t^37 - 21*t^36 - 21*t^35 -
%F A170608 21*t^34 - 21*t^33 - 21*t^32 - 21*t^31 - 21*t^30 - 21*t^29 - 21*t^28 -
%F A170608 21*t^27 - 21*t^26 - 21*t^25 - 21*t^24 - 21*t^23 - 21*t^22 - 21*t^21 -
%F A170608 21*t^20 - 21*t^19 - 21*t^18 - 21*t^17 - 21*t^16 - 21*t^15 - 21*t^14 -
%F A170608 21*t^13 - 21*t^12 - 21*t^11 - 21*t^10 - 21*t^9 - 21*t^8 - 21*t^7 -
%F A170608 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1)
%t A170608 coxG[{48,231,-21}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 25 2019 *)
%K A170608 nonn
%O A170608 0,2
%A A170608 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009