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A169377 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169377 #15 Oct 11 2024 06:58:44
%S A169377 1,28,756,20412,551124,14880348,401769396,10847773692,292889889684,
%T A169377 7908027021468,213516729579636,5764951698650172,155653695863554644,
%U A169377 4202649788315975388,113471544284531335476,3063731695682346057852
%N A169377 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169377 The initial terms coincide with those of A170747, although the two sequences are eventually different.
%C A169377 First disagreement at index 31: a(31) = 244382979906455947924959129425348365521160194, A170747(31) = 244382979906455947924959129425348365521160572. - _Klaus Brockhaus_, Jun 17 2011
%C A169377 Computed with Magma using commands similar to those used to compute A154638.
%H A169377 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, -351).
%F A169377 G.f.: (t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 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 + 2*t^2 + 2*t + 1)/(351*t^31 - 26*t^30 - 26*t^29 - 26*t^28 - 26*t^27 - 26*t^26 - 26*t^25 - 26*t^24 - 26*t^23 - 26*t^22 - 26*t^21 - 26*t^20 - 26*t^19 - 26*t^18 - 26*t^17 - 26*t^16 - 26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).
%t A169377 coxG[{31,351,-26}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 05 2022 *)
%Y A169377 Cf. A170747 (G.f.: (1+x)/(1-27*x)).
%K A169377 nonn
%O A169377 0,2
%A A169377 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009