cp's OEIS Frontend

A170183 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

%I A170183 #21 Sep 08 2022 08:45:49
%S A170183 1,30,870,25230,731670,21218430,615334470,17844699630,517496289270,
%T A170183 15007392388830,435214379276070,12621216999006030,366015292971174870,
%U A170183 10614443496164071230,307818861388758065670,8926746980273983904430
%N A170183 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
%C A170183 The initial terms coincide with those of A170749, although the two sequences are eventually different.
%C A170183 First disagreement is at index 39, the difference is 435. - _Vincenzo Librandi_, Dec 10 2009
%C A170183 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170183 Vincenzo Librandi, <a href="/A170183/b170183.txt">Table of n, a(n) for n = 0..100</a>
%H A170183 <a href="/index/Rec#order_39">Index entries for linear recurrences with constant coefficients</a>, signature (28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, -406).
%F A170183 G.f.: (t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*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) /(406*t^39 - 28*t^38 - 28*t^37 - 28*t^36 - 28*t^35 - 28*t^34 - 28*t^33 - 28*t^32 - 28*t^31 - 28*t^30 - 28*t^29 - 28*t^28 - 28*t^27 - 28*t^26 - 28*t^25 - 28*t^24 - 28*t^23 - 28*t^22 - 28*t^21 - 28*t^20 - 28*t^19 - 28*t^18 - 28*t^17 - 28*t^16 - 28*t^15 - 28*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1)
%t A170183 With[{num=Total[2t^Range[38]]+t^39+1,den=Total[-28 t^Range[38]]+ 406t^39+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Sep 20 2011 *)
%o A170183 (Magma) /* Alternatively */ m:=16; R<t>:=PowerSeriesRing(Integers(), m); Coefficients(R!((t^40+t^39-t-1)/(406*t^40-434*t^39+29*t-1)));  // _Bruno Berselli_, Sep 20 2011
%Y A170183 Cf. A170749.
%K A170183 nonn
%O A170183 0,2
%A A170183 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009