A168705 - OEIS

%I #13 Jun 01 2017 09:00:54

%S 1,28,756,20412,551124,14880348,401769396,10847773692,292889889684,

%T 7908027021468,213516729579636,5764951698650172,155653695863554644,

%U 4202649788315975388,113471544284531335476,3063731695682346057852

%N Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%C The initial terms coincide with those of A170747, although the two sequences are eventually different.

%C First disagreement at index 17: a(17) = 2233460406152430276173730, A170747(17) = 2233460406152430276174108. - _Klaus Brockhaus_, Mar 30 2011

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

%H G. C. Greubel, <a href="/A168705/b168705.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, -351).

%F G.f.: (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)/(351*t^17 - 26*t^16 - 26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).

%t CoefficientList[Series[(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)/(351*t^17 - 26*t^16 - 26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Aug 04 2016 *)

%t coxG[{17,351,-26}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 01 2017 *)

%Y Cf. A170747 (G.f.: (1+x)/(1-27*x)).

%K nonn

%O 0,2

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