A170331 - OEIS

%I #10 Jul 05 2021 19:41:41

%S 1,34,1122,37026,1221858,40321314,1330603362,43909910946,

%T 1449027061218,47817893020194,1577990469666402,52073685498991266,

%U 1718431621466711778,56708243508401488674,1871372035777249126242,61755277180649221165986

%N Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

%C The initial terms coincide with those of A170753, although the two sequences are eventually different.

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

%H <a href="/index/Rec#order_42">Index entries for linear recurrences with constant coefficients</a>, signature (32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, -528).

%F G.f. (t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +

%F 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +

%F 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +

%F 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +

%F 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 +

%F 2*t + 1)/(528*t^42 - 32*t^41 - 32*t^40 - 32*t^39 - 32*t^38 - 32*t^37 -

%F 32*t^36 - 32*t^35 - 32*t^34 - 32*t^33 - 32*t^32 - 32*t^31 - 32*t^30 -

%F 32*t^29 - 32*t^28 - 32*t^27 - 32*t^26 - 32*t^25 - 32*t^24 - 32*t^23 -

%F 32*t^22 - 32*t^21 - 32*t^20 - 32*t^19 - 32*t^18 - 32*t^17 - 32*t^16 -

%F 32*t^15 - 32*t^14 - 32*t^13 - 32*t^12 - 32*t^11 - 32*t^10 - 32*t^9 -

%F 32*t^8 - 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1)

%t With[{num=Total[2t^Range[41]]+t^42+1,den=Total[-32 t^Range[41]]+528t^42+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Apr 10 2014 *)

%t coxG[{42,528,-32}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 05 2021 *)

%K nonn

%O 0,2

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