%I #12 May 10 2018 02:00:11

%S 1,16,240,3600,54000,810000,12150000,182250000,2733750000,41006250000,

%T 615093750000,9226406250000,138396093750000,2075941406250000,

%U 31139121093750000,467086816406250000,7006302246093750000

%N Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.

%C The initial terms coincide with those of A170735, although the two sequences are eventually different.

%C First disagreement at index 29: a(29) = 13635630878782868385314941406249880, A170735(29) = 13635630878782868385314941406250000. - _Klaus Brockhaus_, Jun 03 2011

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

%H <a href="/index/Rec#order_29">Index entries for linear recurrences with constant coefficients</a>, signature (14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, -105).

%F G.f.: (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)/(105*t^29 - 14*t^28 - 14*t^27 - 14*t^26 - 14*t^25 - 14*t^24 - 14*t^23 - 14*t^22 - 14*t^21 - 14*t^20 - 14*t^19 - 14*t^18 - 14*t^17 - 14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).

%t coxG[{29,105,-14}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Feb 09 2015 *)

%Y Cf. A170735 (G.f.: (1+x)/(1-15*x)).

%K nonn

%O 0,2

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