A169001 - OEIS

%I #10 Apr 08 2019 11:26:40

%S 1,36,1260,44100,1543500,54022500,1890787500,66177562500,

%T 2316214687500,81067514062500,2837362992187500,99307704726562500,

%U 3475769665429687500,121651938290039062500,4257817840151367187500,149023624405297851562500

%N Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

%C The initial terms coincide with those of A170755, although the two sequences are eventually different.

%C First disagreement at index 23: a(23) = 335582632420033382806777954101561870, A170755(23) = 335582632420033382806777954101562500. - Klaus Brockhaus, Apr 19 2011

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

%H <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, -595).

%F G.f.: (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)/(595*t^23 - 34*t^22 - 34*t^21 - 34*t^20 - 34*t^19 - 34*t^18 - 34*t^17 - 34*t^16 - 34*t^15 - 34*t^14 - 34*t^13 - 34*t^12 - 34*t^11 - 34*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).

%t coxG[{23,595,-34}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 08 2019 *)

%Y Cf. A170755 (G.f.: (1+x)/(1-35*x)).

%K nonn

%O 0,2

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