cp's OEIS Frontend

A170024 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

%I A170024 #8 Jul 17 2019 17:55:33
%S A170024 1,15,210,2940,41160,576240,8067360,112943040,1581202560,22136835840,
%T A170024 309915701760,4338819824640,60743477544960,850408685629440,
%U A170024 11905721598812160,166680102383370240,2333521433367183360
%N A170024 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
%C A170024 The initial terms coincide with those of A170734, although the two sequences are eventually different.
%C A170024 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170024 <a href="/index/Rec#order_36">Index entries for linear recurrences with constant coefficients</a>, signature (13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, -91).
%F A170024 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 A170024 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 A170024 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 A170024 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 A170024 + 2*t^3 + 2*t^2 + 2*t + 1)/(91*t^36 - 13*t^35 - 13*t^34 - 13*t^33 -
%F A170024 13*t^32 - 13*t^31 - 13*t^30 - 13*t^29 - 13*t^28 - 13*t^27 - 13*t^26 -
%F A170024 13*t^25 - 13*t^24 - 13*t^23 - 13*t^22 - 13*t^21 - 13*t^20 - 13*t^19 -
%F A170024 13*t^18 - 13*t^17 - 13*t^16 - 13*t^15 - 13*t^14 - 13*t^13 - 13*t^12 -
%F A170024 13*t^11 - 13*t^10 - 13*t^9 - 13*t^8 - 13*t^7 - 13*t^6 - 13*t^5 - 13*t^4
%F A170024 - 13*t^3 - 13*t^2 - 13*t + 1)
%t A170024 coxG[{36,91,-13}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 17 2019 *)
%K A170024 nonn
%O A170024 0,2
%A A170024 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009