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Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.
1

%I #12 Nov 26 2016 16:36:37

%S 1,3,6,12,24,48,96,192,384,768,1536,3072,6144,12288,24576,49149,98292,

%T 196575,393132,786228,1572384,3144624,6288960,12577344,25153536,

%U 50304768,100604928,201200640,402382848,804728832,1609383942,3218620449

%N Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.

%C The initial terms coincide with those of A003945, 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="/A167648/b167648.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1).

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

%t CoefficientList[Series[(t^14 + t^13 + t^12 + t^11 + t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1)/(t^14 - 2*t^13 + t^12 - 2*t^11 + t^10 - 2*t^9 + t^8 - 2*t^7 + t^6 - 2*t^5 + t^4 - 2*t^3 + t^2 - 2*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Jun 18 2016 *)

%K nonn

%O 0,2

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