A169137 - OEIS

%I #10 May 05 2021 14:42:19

%S 1,28,756,20412,551124,14880348,401769396,10847773692,292889889684,

%T 7908027021468,213516729579636,5764951698650172,155653695863554644,

%U 4202649788315975388,113471544284531335476,3063731695682346057852

%N Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

%C The initial terms coincide with those of A170747, although the two sequences are eventually different.

%C First disagreement at index 26: a(26) = 17031470055974015855351151793328116218, A170747(26) = 17031470055974015855351151793328116596. - Klaus Brockhaus, Apr 30 2011

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

%H <a href="/index/Rec#order_26">Index entries for linear recurrences with constant coefficients</a>, signature (26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, -351).

%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)/(351*t^26 - 26*t^25 - 26*t^24 - 26*t^23 - 26*t^22 - 26*t^21 - 26*t^20 - 26*t^19 - 26*t^18 - 26*t^17 - 26*t^16 - 26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).

%t coxG[{26,351,-26}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, May 05 2021 *)

%Y Cf. A170747 (G.f.: (1+x)/(1-27*x)).

%K nonn

%O 0,2

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