cp's OEIS Frontend

A169328 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

%I A169328 #12 May 10 2018 00:23:01
%S A169328 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,
%T A169328 5638330743552,146596599332352,3811511582641152,99099301148669952,
%U A169328 2576581829865418752,66991127576500887552,1741769316989023076352
%N A169328 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
%C A169328 The initial terms coincide with those of A170746, although the two sequences are eventually different.
%C A169328 First disagreement at index 30: a(30) = 2921398859026466916153183376908893502308001, A170746(30) = 2921398859026466916153183376908893502308352. - _Klaus Brockhaus_, Jun 23 2011
%C A169328 Computed with Magma using commands similar to those used to compute A154638.
%H A169328 <a href="/index/Rec#order_30">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, 25, -325).
%F A169328 G.f.: (t^30 + 2*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^30 - 25*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 A169328 coxG[{30,325,-25}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 07 2015 *)
%Y A169328 Cf. A170746 (G.f.: (1+x)/(1-26*x)).
%K A169328 nonn
%O A169328 0,2
%A A169328 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009