cp's OEIS Frontend

A170080 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

%I A170080 #8 Jul 08 2017 11:58:29
%S A170080 1,23,506,11132,244904,5387888,118533536,2607737792,57370231424,
%T A170080 1262145091328,27767192009216,610878224202752,13439320932460544,
%U A170080 295665060514131968,6504631331310903296,143101889288839872512
%N A170080 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
%C A170080 The initial terms coincide with those of A170742, although the two sequences are eventually different.
%C A170080 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170080 <a href="/index/Rec#order_37">Index entries for linear recurrences with constant coefficients</a>, signature (21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -231).
%F A170080 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 A170080 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 A170080 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 A170080 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 A170080 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(231*t^37 - 21*t^36 - 21*t^35 -
%F A170080 21*t^34 - 21*t^33 - 21*t^32 - 21*t^31 - 21*t^30 - 21*t^29 - 21*t^28 -
%F A170080 21*t^27 - 21*t^26 - 21*t^25 - 21*t^24 - 21*t^23 - 21*t^22 - 21*t^21 -
%F A170080 21*t^20 - 21*t^19 - 21*t^18 - 21*t^17 - 21*t^16 - 21*t^15 - 21*t^14 -
%F A170080 21*t^13 - 21*t^12 - 21*t^11 - 21*t^10 - 21*t^9 - 21*t^8 - 21*t^7 -
%F A170080 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1)
%t A170080 coxG[{37,231,-21}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 08 2017 *)
%K A170080 nonn
%O A170080 0,2
%A A170080 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009