cp's OEIS Frontend

A169396 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

%I A169396 #13 Oct 12 2024 01:40:46
%S A169396 1,47,2162,99452,4574792,210440432,9680259872,445291954112,
%T A169396 20483429889152,942237774900992,43342937645445632,1993775131690499072,
%U A169396 91713656057762957312,4218828178657096036352,194066096218226417672192
%N A169396 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
%C A169396 The initial terms coincide with those of A170766, although the two sequences are eventually different.
%C A169396 First disagreement at index 31: a(31) = 3587837860113843800913027235784288878110445112654791, A170766(31) = 3587837860113843800913027235784288878110445112655872. - _Klaus Brockhaus_, Jun 17 2011
%C A169396 Computed with Magma using commands similar to those used to compute A154638.
%H A169396 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, signature (45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, -1035).
%F A169396 G.f.: (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)/(1035*t^31 - 45*t^30 - 45*t^29 - 45*t^28 - 45*t^27 - 45*t^26 - 45*t^25 - 45*t^24 - 45*t^23 - 45*t^22 - 45*t^21 - 45*t^20 - 45*t^19 - 45*t^18 - 45*t^17 - 45*t^16 - 45*t^15 - 45*t^14 - 45*t^13 - 45*t^12 - 45*t^11 - 45*t^10 - 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).
%Y A169396 Cf. A170766 (G.f.: (1+x)/(1-46*x)).
%K A169396 nonn
%O A169396 0,2
%A A169396 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009