cp's OEIS Frontend

A170358 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

%I A170358 #8 Nov 21 2016 19:16:51
%S A170358 1,13,156,1872,22464,269568,3234816,38817792,465813504,5589762048,
%T A170358 67077144576,804925734912,9659108818944,115909305827328,
%U A170358 1390911669927936,16690940039135232,200291280469622784
%N A170358 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
%C A170358 The initial terms coincide with those of A170732, although the two sequences are eventually different.
%C A170358 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170358 <a href="/index/Rec#order_43">Index entries for linear recurrences with constant coefficients</a>, signature (11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, -66).
%F A170358 G.f. (t^43 + 2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 +
%F A170358 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 +
%F A170358 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 +
%F A170358 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 +
%F A170358 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3
%F A170358 + 2*t^2 + 2*t + 1)/(66*t^43 - 11*t^42 - 11*t^41 - 11*t^40 - 11*t^39 -
%F A170358 11*t^38 - 11*t^37 - 11*t^36 - 11*t^35 - 11*t^34 - 11*t^33 - 11*t^32 -
%F A170358 11*t^31 - 11*t^30 - 11*t^29 - 11*t^28 - 11*t^27 - 11*t^26 - 11*t^25 -
%F A170358 11*t^24 - 11*t^23 - 11*t^22 - 11*t^21 - 11*t^20 - 11*t^19 - 11*t^18 -
%F A170358 11*t^17 - 11*t^16 - 11*t^15 - 11*t^14 - 11*t^13 - 11*t^12 - 11*t^11 -
%F A170358 11*t^10 - 11*t^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 -
%F A170358 11*t^2 - 11*t + 1)
%t A170358 With[{num=Total[2t^Range[42]]+t^43+1,den=Total[-11 t^Range[42]]+66t^43+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* _Harvey P. Dale_, May 29 2013 *)
%K A170358 nonn
%O A170358 0,2
%A A170358 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009