A169133 - OEIS

%I #15 Dec 03 2025 17:11:33

%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)^26 = I.

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

%C First disagreement at index 26: a(26) = 265098421726069091188171497832558356, A170743(26) = 265098421726069091188171497832558632. - Klaus Brockhaus, Apr 30 2011

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

%H Vincenzo Librandi, <a href="/A169133/b169133.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_26">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, 22, 22, 22, 22, 22, 22, 22, 22, 22, -253).

%F G.f.: (t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*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)/(253*t^26 - 22*t^25 - 22*t^24 - 22*t^23 - 22*t^22 - 22*t^21 - 22*t^20 - 22*t^19 - 22*t^18 - 22*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 With[{num=Total[2t^Range[25]]+t^26+1,den=Total[-22 t^Range[25]]+ 253t^26+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Feb 27 2012 *)

%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