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Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.
1

%I #12 Nov 24 2016 11:09:56

%S 1,31,930,27900,837000,25110000,753300000,22599000000,677970000000,

%T 20339100000000,610173000000000,18305190000000000,549155700000000000,

%U 16474671000000000000,494240130000000000000,14827203899999999999535

%N Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.

%C The initial terms coincide with those of A170750, although the two sequences are eventually different.

%C Computed with MAGMA using commands similar to those used to compute A154638.

%H G. C. Greubel, <a href="/A167756/b167756.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, -435).

%F G.f.: (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)/(435*t^15 - 29*t^14 - 29*t^13 - 29*t^12 - 29*t^11 - 29*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).

%t CoefficientList[Series[(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)/(435*t^15 - 29*t^14 - 29*t^13 - 29*t^12 - 29*t^11 - 29*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Jun 23 2016 *)

%t coxG[{15,435,-29}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 20 2016 *)

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009