A168818 - OEIS

%I #15 Nov 26 2020 15:34:11

%S 1,45,1980,87120,3833280,168664320,7421230080,326534123520,

%T 14367501434880,632170063134720,27815482777927680,1223881242228817920,

%U 53850774658067988480,2369434084954991493120,104255099738019625697280

%N Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%C The initial terms coincide with those of A170764, although the two sequences are eventually different.

%C First disagreement at index 19: a(19) = 17193357381537585907888784669730, A170764(19) = 17193357381537585907888784670720. - _Klaus Brockhaus_, Apr 01 2011

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

%H G. C. Greubel, <a href="/A168818/b168818.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, -946).

%F G.f.: (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)/(946*t^19 - 43*t^18 - 43*t^17 - 43*t^16 - 43*t^15 - 43*t^14 - 43*t^13 - 43*t^12 - 43*t^11 - 43*t^10 - 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).

%t CoefficientList[Series[(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)/(946*t^19 - 43*t^18 - 43*t^17 - 43*t^16 - 43*t^15 - 43*t^14 - 43*t^13 - 43*t^12 - 43*t^11 - 43*t^10 - 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Nov 21 2016 *)

%t coxG[{19,946,-43}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 26 2020 *)

%Y Cf. A170764 (G.f.: (1+x)/(1-44*x)).

%K nonn,easy

%O 0,2

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