login
Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.
1

%I #9 Nov 24 2016 09:38:11

%S 1,17,272,4352,69632,1114112,17825792,285212672,4563402752,

%T 73014444032,1168231104512,18691697672192,299067162754936,

%U 4785074604076800,76561193665194120,1224979098642551040,19599665578271938560

%N Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

%C The initial terms coincide with those of A170736, 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="/A166585/b166585.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, -120).

%F G.f.: (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)/(120*t^12 - 15*t^11 - 15*t^10 - 15*t^9 -15*t^8 - 15*t^7 - 15*t^6 - 15*t^5 - 15*t^4 - 15*t^3 - 15*t^2 -15*t +1).

%t CoefficientList[Series[(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)/(120*t^12 - 15*t^11 - 15*t^10 - 15*t^9 - 15*t^8 - 15*t^7 - 15*t^6 - 15*t^5 - 15*t^4 - 15*t^3 - 15*t^2 - 15*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, May 17 2016 *)

%K nonn

%O 0,2

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