A169234 - OEIS

%I #12 Jun 03 2023 11:50:42

%S 1,29,812,22736,636608,17825024,499100672,13974818816,391294926848,

%T 10956257951744,306775222648832,8589706234167296,240511774556684288,

%U 6734329687587160064,188561231252440481792,5279714475068333490176

%N Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

%C The initial terms coincide with those of A170748, although the two sequences are eventually different.

%C First disagreement at index 28: a(28) = 34329291795869566821950325690984770305642, A170748(28) = 34329291795869566821950325690984770306048. - _Klaus Brockhaus_, May 24 2011

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

%H <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, -378).

%F G.f.: (t^28 + 2*t^27 + 2*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)/(378*t^28 - 27*t^27 - 27*t^26 - 27*t^25 - 27*t^24 - 27*t^23 - 27*t^22 - 27*t^21 - 27*t^20 - 27*t^19 - 27*t^18 - 27*t^17 - 27*t^16 - 27*t^15 - 27*t^14 - 27*t^13 - 27*t^12 - 27*t^11 - 27*t^10 - 27*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).

%t coxG[{28,378,-27}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 03 2023 *)

%Y Cf. A170748 (G.f.: (1+x)/(1-28*x)).

%K nonn

%O 0,2

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