cp's OEIS Frontend

A169042 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.

%I A169042 #10 Aug 27 2017 12:39:23
%S A169042 1,29,812,22736,636608,17825024,499100672,13974818816,391294926848,
%T A169042 10956257951744,306775222648832,8589706234167296,240511774556684288,
%U A169042 6734329687587160064,188561231252440481792,5279714475068333490176
%N A169042 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
%C A169042 The initial terms coincide with those of A170748, although the two sequences are eventually different.
%C A169042 First disagreement at index 24: a(24) = 55851227021081005996769454281719402, A170748(24) = 55851227021081005996769454281719808. - Klaus Brockhaus, Apr 20 2011
%C A169042 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169042 <a href="/index/Rec#order_24">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, -378).
%F A169042 G.f.: (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^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 A169042 coxG[{24,378,-27}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 27 2017 *)
%Y A169042 Cf. A170748 (G.f.: (1+x)/(1-28*x)).
%K A169042 nonn
%O A169042 0,2
%A A169042 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009