A167370 - OEIS

%I #13 Jul 04 2017 13:11:52

%S 1,30,870,25230,731670,21218430,615334470,17844699630,517496289270,

%T 15007392388830,435214379276070,12621216999006030,366015292971174870,

%U 10614443496164071230,307818861388758065235,8926746980273983879200,258875662427945532131400

%N Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^14 = I.

%C The initial terms coincide with those of A170749, 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="/A167370/b167370.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 (28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, -406).

%F G.f.: (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)/(406*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).

%t CoefficientList[Series[(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)/ (406*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Jun 11 2016 *)

%t coxG[{14,406,-28}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 04 2017 *)

%Y Cf. A154638, A170749.

%K nonn

%O 0,2

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