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A169569 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

%I A169569 #8 Jun 01 2021 13:01:37
%S A169569 1,28,756,20412,551124,14880348,401769396,10847773692,292889889684,
%T A169569 7908027021468,213516729579636,5764951698650172,155653695863554644,
%U A169569 4202649788315975388,113471544284531335476,3063731695682346057852
%N A169569 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
%C A169569 The initial terms coincide with those of A170747, although the two sequences are eventually different.
%C A169569 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169569 <a href="/index/Rec#order_35">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, 26, 26, 26, 26, -351).
%F A169569 G.f. (t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A169569 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 A169569 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 A169569 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 A169569 + 2*t^2 + 2*t + 1)/(351*t^35 - 26*t^34 - 26*t^33 - 26*t^32 - 26*t^31 -
%F A169569 26*t^30 - 26*t^29 - 26*t^28 - 26*t^27 - 26*t^26 - 26*t^25 - 26*t^24 -
%F A169569 26*t^23 - 26*t^22 - 26*t^21 - 26*t^20 - 26*t^19 - 26*t^18 - 26*t^17 -
%F A169569 26*t^16 - 26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 -
%F A169569 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 -
%F A169569 26*t + 1)
%t A169569 coxG[{35,351,-26}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 01 2021 *)
%K A169569 nonn
%O A169569 0,2
%A A169569 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009