A168701 - OEIS

%I #13 Nov 24 2016 13:06:41

%S 1,24,552,12696,292008,6716184,154472232,3552861336,81715810728,

%T 1879463646744,43227663875112,994236269127576,22867434189934248,

%U 525950986368487704,12096872686475217192,278228071788929995416

%N Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

%C The initial terms coincide with those of A170743, although the two sequences are eventually different.

%C First disagreement at index 17: a(17) = 147182649976343967574788, A170743(17) = 147182649976343967575064. - _Klaus Brockhaus_, Mar 30 2011

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

%H G. C. Greubel, <a href="/A168701/b168701.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, -253).

%F G.f.: (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)/( 253*t^17 - 22*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 -22*t^5 -22*t^4 -22*t^3 -22*t^2 -22*t +1).

%t coxG[{17,253,-22}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Apr 29 2016 *)

%t CoefficientList[Series[(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)/(253*t^17 - 22*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1), {t,0,50}], t] (* _G. C. Greubel_, Aug 04 2016 *)

%Y Cf. A170743 (G.f.: (1+x)/(1-23*x)).

%K nonn

%O 0,2

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