cp's OEIS Frontend

A170086 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

%I A170086 #13 Feb 24 2024 11:08:59
%S A170086 1,29,812,22736,636608,17825024,499100672,13974818816,391294926848,
%T A170086 10956257951744,306775222648832,8589706234167296,240511774556684288,
%U A170086 6734329687587160064,188561231252440481792,5279714475068333490176,147832005301913337724928,4139296148453573456297984
%N A170086 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
%C A170086 The initial terms coincide with those of A170748, although the two sequences are eventually different.
%C A170086 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170086 <a href="/index/Rec#order_37">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, 27, 27, 27, 27, 27, 27, 27, 27, 27, -378).
%F A170086 G.f. (t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 +
%F A170086 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 +
%F A170086 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 +
%F A170086 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 +
%F A170086 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(378*t^37 - 27*t^36 - 27*t^35 -
%F A170086 27*t^34 - 27*t^33 - 27*t^32 - 27*t^31 - 27*t^30 - 27*t^29 - 27*t^28 -
%F A170086 27*t^27 - 27*t^26 - 27*t^25 - 27*t^24 - 27*t^23 - 27*t^22 - 27*t^21 -
%F A170086 27*t^20 - 27*t^19 - 27*t^18 - 27*t^17 - 27*t^16 - 27*t^15 - 27*t^14 -
%F A170086 27*t^13 - 27*t^12 - 27*t^11 - 27*t^10 - 27*t^9 - 27*t^8 - 27*t^7 -
%F A170086 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1)
%t A170086 With[{num=Total[2t^Range[36]]+t^37+1,den=Total[-27 t^Range[36]]+ 378t^37+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Mar 28 2012 *)
%Y A170086 Cf. A154638, A170748.
%K A170086 nonn
%O A170086 0,2
%A A170086 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009