cp's OEIS Frontend

A170072 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

%I A170072 #8 Aug 11 2019 13:58:06
%S A170072 1,15,210,2940,41160,576240,8067360,112943040,1581202560,22136835840,
%T A170072 309915701760,4338819824640,60743477544960,850408685629440,
%U A170072 11905721598812160,166680102383370240,2333521433367183360
%N A170072 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
%C A170072 The initial terms coincide with those of A170734, although the two sequences are eventually different.
%C A170072 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170072 <a href="/index/Rec#order_37">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, 13, -91).
%F A170072 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 A170072 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 A170072 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 A170072 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 A170072 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(91*t^37 - 13*t^36 - 13*t^35 -
%F A170072 13*t^34 - 13*t^33 - 13*t^32 - 13*t^31 - 13*t^30 - 13*t^29 - 13*t^28 -
%F A170072 13*t^27 - 13*t^26 - 13*t^25 - 13*t^24 - 13*t^23 - 13*t^22 - 13*t^21 -
%F A170072 13*t^20 - 13*t^19 - 13*t^18 - 13*t^17 - 13*t^16 - 13*t^15 - 13*t^14 -
%F A170072 13*t^13 - 13*t^12 - 13*t^11 - 13*t^10 - 13*t^9 - 13*t^8 - 13*t^7 -
%F A170072 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1)
%t A170072 coxG[{37,91,-13}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 11 2019 *)
%K A170072 nonn
%O A170072 0,2
%A A170072 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009