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%I #18 Apr 27 2021 19:17:51
%S 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,
%T 9663676416,77309411328,618475290624,4947802324992,39582418599936,
%U 316659348799488,2533274790395904,20266198323167232,162129586585337856
%N Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C The initial terms coincide with those of A003951, although the two sequences are eventually different.
%C First disagreement at index 31: a(31) = 11141460353568422474092117980, A003951(31) = 11141460353568422474092118016. - _Klaus Brockhaus_, Jun 17 2011
%C Computed with Magma using commands similar to those used to compute A154638.
%H <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,-28).
%F 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)/(28*t^31 - 7*t^30 - 7*t^29 - 7*t^28 - 7*t^27 - 7*t^26 - 7*t^25 - 7*t^24 - 7*t^23 - 7*t^22 - 7*t^21 - 7*t^20 - 7*t^19 - 7*t^18 - 7*t^17 - 7*t^16 - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1).
%F a(n) = -28*a(n-31) + 7*Sum_{k=1..30} a(n-k). - _Wesley Ivan Hurt_, Apr 26 2021
%Y Cf. A003951 (G.f.: (1+x)/(1-8*x)).
%K nonn
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
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