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A170469 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.

%I A170469 #8 Nov 21 2016 16:57:16
%S A170469 1,28,756,20412,551124,14880348,401769396,10847773692,292889889684,
%T A170469 7908027021468,213516729579636,5764951698650172,155653695863554644,
%U A170469 4202649788315975388,113471544284531335476,3063731695682346057852
%N A170469 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
%C A170469 The initial terms coincide with those of A170747, although the two sequences are eventually different.
%C A170469 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170469 <a href="/index/Rec#order_45">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, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, -351).
%F A170469 G.f. (t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 +
%F A170469 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170469 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 +
%F A170469 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 +
%F A170469 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 +
%F A170469 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(351*t^45 - 26*t^44 - 26*t^43 -
%F A170469 26*t^42 - 26*t^41 - 26*t^40 - 26*t^39 - 26*t^38 - 26*t^37 - 26*t^36 -
%F A170469 26*t^35 - 26*t^34 - 26*t^33 - 26*t^32 - 26*t^31 - 26*t^30 - 26*t^29 -
%F A170469 26*t^28 - 26*t^27 - 26*t^26 - 26*t^25 - 26*t^24 - 26*t^23 - 26*t^22 -
%F A170469 26*t^21 - 26*t^20 - 26*t^19 - 26*t^18 - 26*t^17 - 26*t^16 - 26*t^15 -
%F A170469 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 -
%F A170469 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1)
%t A170469 coxG[{45,351,-26}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 05 2016 *)
%K A170469 nonn
%O A170469 0,2
%A A170469 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009