A168799 - OEIS

%I #16 Oct 18 2020 17:37:14

%S 1,26,650,16250,406250,10156250,253906250,6347656250,158691406250,

%T 3967285156250,99182128906250,2479553222656250,61988830566406250,

%U 1549720764160156250,38743019104003906250,968575477600097656250

%N Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%C The initial terms coincide with those of A170745, although the two sequences are eventually different.

%C First disagreement at index 19: a(19) = 378349795937538146972655925, A170745(19) = 378349795937538146972656250. - _Klaus Brockhaus_, Apr 01 2011

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

%H G. C. Greubel, <a href="/A168799/b168799.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 (24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, -300).

%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)/(300*t^19 - 24*t^18 - 24*t^17 - 24*t^16 - 24*t^15 - 24*t^14 - 24*t^13 - 24*t^12 - 24*t^11 - 24*t^10 - 24*t^9 - 24*t^8 - 24*t^7 - 24*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*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)/(300*t^19 - 24*t^18 - 24*t^17 - 24*t^16 - 24*t^15 - 24*t^14 - 24*t^13 - 24*t^12 - 24*t^11 - 24*t^10 - 24*t^9 - 24*t^8 - 24*t^7 - 24*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1), {t, 0, 50}], t] (* _G. C. Greubel_, Aug 16 2016 *)

%t coxG[{19,300,-24}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Oct 18 2020 *)

%Y Cf. A170745 (G.f.: (1+x)/(1-25*x)).

%K nonn

%O 0,2

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