A169213 - OEIS

%I #17 May 10 2018 02:19:47

%S 1,8,56,392,2744,19208,134456,941192,6588344,46118408,322828856,

%T 2259801992,15818613944,110730297608,775112083256,5425784582792,

%U 37980492079544,265863444556808,1861044111897656,13027308783283592

%N Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

%C The initial terms coincide with those of A003950, although the two sequences are eventually different.

%C First disagreement at index 28: a(28) = 525698898908274241116316, A003950(28) = 525698898908274241116344. - _Klaus Brockhaus_, May 24 2011

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

%H Vincenzo Librandi, <a href="/A169213/b169213.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -21).

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

%t With[{num=Total[2t^Range[27]]+t^28+1,den=Total[-6 t^Range[27]]+21t^28+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Feb 10 2014 *)

%Y Cf. A003950 (G.f.: (1+x)/(1-7*x)).

%K nonn

%O 0,2

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