cp's OEIS Frontend

A170094 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

%I A170094 #8 Jun 12 2017 18:28:07
%S A170094 1,37,1332,47952,1726272,62145792,2237248512,80540946432,
%T A170094 2899474071552,104381066575872,3757718396731392,135277862282330112,
%U A170094 4870003042163884032,175320109517899825152,6311523942644393705472
%N A170094 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
%C A170094 The initial terms coincide with those of A170756, although the two sequences are eventually different.
%C A170094 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170094 <a href="/index/Rec#order_37">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, 35, -630).
%F A170094 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 A170094 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 A170094 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 A170094 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 A170094 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(630*t^37 - 35*t^36 - 35*t^35 -
%F A170094 35*t^34 - 35*t^33 - 35*t^32 - 35*t^31 - 35*t^30 - 35*t^29 - 35*t^28 -
%F A170094 35*t^27 - 35*t^26 - 35*t^25 - 35*t^24 - 35*t^23 - 35*t^22 - 35*t^21 -
%F A170094 35*t^20 - 35*t^19 - 35*t^18 - 35*t^17 - 35*t^16 - 35*t^15 - 35*t^14 -
%F A170094 35*t^13 - 35*t^12 - 35*t^11 - 35*t^10 - 35*t^9 - 35*t^8 - 35*t^7 -
%F A170094 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1)
%t A170094 coxG[{37,630,-35}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jun 12 2017 *)
%K A170094 nonn
%O A170094 0,2
%A A170094 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009