cp's OEIS Frontend

A170078 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

%I A170078 #8 Nov 26 2016 10:03:20
%S A170078 1,21,420,8400,168000,3360000,67200000,1344000000,26880000000,
%T A170078 537600000000,10752000000000,215040000000000,4300800000000000,
%U A170078 86016000000000000,1720320000000000000,34406400000000000000
%N A170078 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
%C A170078 The initial terms coincide with those of A170740, although the two sequences are eventually different.
%C A170078 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170078 <a href="/index/Rec#order_37">Index entries for linear recurrences with constant coefficients</a>, signature (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).
%F A170078 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 A170078 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 A170078 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 A170078 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 A170078 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(190*t^37 - 19*t^36 - 19*t^35 -
%F A170078 19*t^34 - 19*t^33 - 19*t^32 - 19*t^31 - 19*t^30 - 19*t^29 - 19*t^28 -
%F A170078 19*t^27 - 19*t^26 - 19*t^25 - 19*t^24 - 19*t^23 - 19*t^22 - 19*t^21 -
%F A170078 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 -
%F A170078 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 -
%F A170078 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1)
%t A170078 With[{num=Total[2t^Range[36]]+t^37+1,den=Total[-19 t^Range[36]]+190t^37+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, Jun 25 2013 *)
%K A170078 nonn
%O A170078 0,2
%A A170078 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009