cp's OEIS Frontend

A168830 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

%I A168830 #16 Apr 12 2019 04:30:51
%S A168830 1,9,72,576,4608,36864,294912,2359296,18874368,150994944,1207959552,
%T A168830 9663676416,77309411328,618475290624,4947802324992,39582418599936,
%U A168830 316659348799488,2533274790395904,20266198323167232,162129586585337856
%N A168830 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
%C A168830 The initial terms coincide with those of A003951, although the two sequences are eventually different.
%C A168830 First disagreement at index 20: a(20) = 1297036692682702812, A003951(20) = 1297036692682702848. - _Klaus Brockhaus_, Apr 01 2011
%C A168830 Computed with MAGMA using commands similar to those used to compute A154638.
%H A168830 G. C. Greubel, <a href="/A168830/b168830.txt">Table of n, a(n) for n = 0..1000</a>
%H A168830 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, -28).
%F A168830 G.f.: (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)/(28*t^20 - 7*t^19 - 7*t^18 - 7*t^17 - 7*t^16 - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1).
%p A168830 (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)/(28*t^20 - 7*t^19 - 7*t^18 - 7*t^17 - 7*t^16 - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1) ;
%p A168830 taylor(%,t=0,65) ;
%p A168830 gfun[seriestolist](%) ; # _R. J. Mathar_, Apr 12 2019
%t A168830 CoefficientList[Series[(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)/(28*t^20 - 7*t^19 - 7*t^18 - 7*t^17 - 7*t^16 - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1), {t,0,100}], t] (* _G. C. Greubel_, Nov 22 2016 *)
%t A168830 coxG[{20,28,-7}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 11 2017 *)
%Y A168830 Cf. A003951 (G.f.: (1+x)/(1-8*x)).
%K A168830 nonn
%O A168830 0,2
%A A168830 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009