A168815 - OEIS

%I #16 Sep 07 2023 17:03:27

%S 1,42,1722,70602,2894682,118681962,4865960442,199504378122,

%T 8179679503002,335366859623082,13750041244546362,563751691026400842,

%U 23113819332082434522,947666592615379815402,38854330297230572431482

%N Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

%C The initial terms coincide with those of A170761, although the two sequences are eventually different.

%C First disagreement at index 19: a(19) = 4501515100636334942966837319021, A170761(19) = 4501515100636334942966837319882. - _Klaus Brockhaus_, Apr 01 2011

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

%H G. C. Greubel, <a href="/A168815/b168815.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 (40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, -820).

%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)/(820*t^19 - 40*t^18 - 40*t^17 - 40*t^16 - 40*t^15 - 40*t^14 - 40*t^13 - 40*t^12 - 40*t^11 - 40*t^10 - 40*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*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)/(820*t^19 -40*t^18 -40*t^17 -40*t^16 -40*t^15 -40*t^14 - 40*t^13 -40*t^12 -40*t^11 -40*t^10 -40*t^9 -40*t^8 -40*t^7 -40*t^6 -40*t^5 - 40*t^4 -40*t^3 -40*t^2 -40*t +1), {t,0,50}], t] (* _G. C. Greubel_, Nov 21 2016 *)

%t coxG[{19,820,-40}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 07 2023 *)

%Y Cf. A170761 (G.f.: (1+x)/(1-41*x)).

%K nonn,easy

%O 0,2

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