A169280 - OEIS

%I #12 Sep 08 2018 20:20:07

%S 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,

%T 5638330743552,146596599332352,3811511582641152,99099301148669952,

%U 2576581829865418752,66991127576500887552,1741769316989023076352

%N Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.

%C The initial terms coincide with those of A170746, although the two sequences are eventually different.

%C First disagreement at index 29: a(29) = 112361494577941035236660899111880519319201, A170746(29) = 112361494577941035236660899111880519319552. - _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 (25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, -325).

%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)/(325*t^29 - 25*t^28 - 25*t^27 - 25*t^26 - 25*t^25 - 25*t^24 - 25*t^23 - 25*t^22 - 25*t^21 - 25*t^20 - 25*t^19 - 25*t^18 - 25*t^17 - 25*t^16 - 25*t^15 - 25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).

%t coxG[{29,325,-25}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 08 2018 *)

%Y Cf. A170746 (G.f.: (1+x)/(1-26*x)).

%K nonn

%O 0,2

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