cp's OEIS Frontend

A170032 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170032 #8 Sep 23 2017 20:04:59
%S A170032 1,23,506,11132,244904,5387888,118533536,2607737792,57370231424,
%T A170032 1262145091328,27767192009216,610878224202752,13439320932460544,
%U A170032 295665060514131968,6504631331310903296,143101889288839872512
%N A170032 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170032 The initial terms coincide with those of A170742, although the two sequences are eventually different.
%C A170032 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170032 <a href="/index/Rec#order_36">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, -231).
%F A170032 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 A170032 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 A170032 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 A170032 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 A170032 + 2*t^3 + 2*t^2 + 2*t + 1)/(231*t^36 - 21*t^35 - 21*t^34 - 21*t^33 -
%F A170032 21*t^32 - 21*t^31 - 21*t^30 - 21*t^29 - 21*t^28 - 21*t^27 - 21*t^26 -
%F A170032 21*t^25 - 21*t^24 - 21*t^23 - 21*t^22 - 21*t^21 - 21*t^20 - 21*t^19 -
%F A170032 21*t^18 - 21*t^17 - 21*t^16 - 21*t^15 - 21*t^14 - 21*t^13 - 21*t^12 -
%F A170032 21*t^11 - 21*t^10 - 21*t^9 - 21*t^8 - 21*t^7 - 21*t^6 - 21*t^5 - 21*t^4
%F A170032 - 21*t^3 - 21*t^2 - 21*t + 1)
%t A170032 coxG[{36,231,-21}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Sep 23 2017 *)
%K A170032 nonn
%O A170032 0,2
%A A170032 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009