cp's OEIS Frontend

A170046 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170046 #8 Nov 26 2016 09:47:15
%S A170046 1,37,1332,47952,1726272,62145792,2237248512,80540946432,
%T A170046 2899474071552,104381066575872,3757718396731392,135277862282330112,
%U A170046 4870003042163884032,175320109517899825152,6311523942644393705472
%N A170046 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170046 The initial terms coincide with those of A170756, although the two sequences are eventually different.
%C A170046 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170046 <a href="/index/Rec#order_36">Index entries for linear recurrences with constant coefficients</a>, signature (35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, -630).
%F A170046 G.f. (t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 +
%F A170046 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 +
%F A170046 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 +
%F A170046 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
%F A170046 + 2*t^3 + 2*t^2 + 2*t + 1)/(630*t^36 - 35*t^35 - 35*t^34 - 35*t^33 -
%F A170046 35*t^32 - 35*t^31 - 35*t^30 - 35*t^29 - 35*t^28 - 35*t^27 - 35*t^26 -
%F A170046 35*t^25 - 35*t^24 - 35*t^23 - 35*t^22 - 35*t^21 - 35*t^20 - 35*t^19 -
%F A170046 35*t^18 - 35*t^17 - 35*t^16 - 35*t^15 - 35*t^14 - 35*t^13 - 35*t^12 -
%F A170046 35*t^11 - 35*t^10 - 35*t^9 - 35*t^8 - 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4
%F A170046 - 35*t^3 - 35*t^2 - 35*t + 1)
%t A170046 coxG[{36,630,-35}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 11 2016 *)
%K A170046 nonn
%O A170046 0,2
%A A170046 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009