A168774 - OEIS

%I #19 Nov 24 2016 14:04:17

%S 1,49,2352,112896,5419008,260112384,12485394432,599298932736,

%T 28766348771328,1380784741023744,66277667569139712,

%U 3181328043318706176,152703746079297896448,7329779811806299029504,351829430966702353416192

%N Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

%C The initial terms coincide with those of A170768, although the two sequences are eventually different.

%C First disagreement at index 18: a(18) = 1867656980614538240112168270696, A170768(18) = 1867656980614538240112168271872. - _Klaus Brockhaus_, Mar 25 2011

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

%H G. C. Greubel, <a href="/A168774/b168774.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, -1128).

%F G.f.: (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)/(1128*t^18 - 47*t^17 - 47*t^16 - 47*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).

%t CoefficientList[Series[(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)/(1128*t^18 - 47*t^17 - 47*t^16 - 47*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 12 2016 *)

%t coxG[{18,1128,-47}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 21 2016 *)

%Y Cf. A170768 (G.f.: (1+x)/(1-48*x)).

%K nonn

%O 0,2

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