A169260 - OEIS

%I #12 May 10 2018 01:56:08

%S 1,7,42,252,1512,9072,54432,326592,1959552,11757312,70543872,

%T 423263232,2539579392,15237476352,91424858112,548549148672,

%U 3291294892032,19747769352192,118486616113152,710919696678912,4265518180073472

%N Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.

%C The initial terms coincide with those of A003949, although the two sequences are eventually different.

%C First disagreement at index 29: a(29) = 42986595501253708480491, A003949(29) = 42986595501253708480512. - _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 (5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, -15).

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

%t With[{num=Total[2t^Range[28]]+t^29+1,den=Total[-5 t^Range[28]]+ 15t^29+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Aug 25 2012 *)

%Y Cf. A003949 (G.f.: (1+x)/(1-6*x)).

%K nonn

%O 0,2

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