A169099 - OEIS

%I #11 Nov 25 2016 12:03:05

%S 1,38,1406,52022,1924814,71218118,2635070366,97497603542,

%T 3607411331054,133474219248998,4938546112212926,182726206151878262,

%U 6760869627619495694,250152176221921340678,9255630520211089605086

%N Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.

%C The initial terms coincide with those of A170757, although the two sequences are eventually different.

%C First disagreement at index 25: a(25) = 1646739770225347068213871371166340459815, A170757(25) = 1646739770225347068213871371166340460518. - Klaus Brockhaus, Apr 25 2011

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

%H <a href="/index/Rec#order_25">Index entries for linear recurrences with constant coefficients</a>, signature (36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, -666).

%F G.f.: (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)/(666*t^25 - 36*t^24 - 36*t^23 - 36*t^22 - 36*t^21 - 36*t^20 - 36*t^19 - 36*t^18 - 36*t^17 - 36*t^16 - 36*t^15 - 36*t^14 - 36*t^13 - 36*t^12 - 36*t^11 - 36*t^10 - 36*t^9 - 36*t^8 - 36*t^7 - 36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1).

%t With[{num=Total[2t^Range[24]]+t^25+1,den=Total[-36 t^Range[24]]+666t^25+1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Mar 26 2012 *)

%Y Cf. A170757 (G.f.: (1+x)/(1-37*x)).

%K nonn

%O 0,2

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