cp's OEIS Frontend

A170495 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.

%I A170495 #10 Aug 09 2025 13:03:03
%S A170495 1,6,30,150,750,3750,18750,93750,468750,2343750,11718750,58593750,
%T A170495 292968750,1464843750,7324218750,36621093750,183105468750,
%U A170495 915527343750,4577636718750,22888183593750,114440917968750,572204589843750
%N A170495 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
%C A170495 The initial terms coincide with those of A003948, although the two sequences are eventually different.
%C A170495 First disagreement at index 46: a(46) = 170530256582424044609069824218735, A003948(46) = 170530256582424044609069824218750.
%C A170495 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170495 <a href="/index/Rec#order_46">Index entries for linear recurrences with constant coefficients</a>, signature (4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -10).
%F A170495 G.f. (t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 +
%F A170495 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 +
%F A170495 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 +
%F A170495 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 +
%F A170495 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 +
%F A170495 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(10*t^46 - 4*t^45 -
%F A170495 4*t^44 - 4*t^43 - 4*t^42 - 4*t^41 - 4*t^40 - 4*t^39 - 4*t^38 - 4*t^37 -
%F A170495 4*t^36 - 4*t^35 - 4*t^34 - 4*t^33 - 4*t^32 - 4*t^31 - 4*t^30 - 4*t^29 -
%F A170495 4*t^28 - 4*t^27 - 4*t^26 - 4*t^25 - 4*t^24 - 4*t^23 - 4*t^22 - 4*t^21 -
%F A170495 4*t^20 - 4*t^19 - 4*t^18 - 4*t^17 - 4*t^16 - 4*t^15 - 4*t^14 - 4*t^13 -
%F A170495 4*t^12 - 4*t^11 - 4*t^10 - 4*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4
%F A170495 - 4*t^3 - 4*t^2 - 4*t + 1)
%t A170495 coxG[{46,10,-4,30}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 09 2025 *)
%Y A170495 Cf. A003948 (g.f.: (1+x)/(1-5*x)).
%K A170495 nonn
%O A170495 0,2
%A A170495 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009