cp's OEIS Frontend

A170214 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.

%I A170214 #8 Nov 22 2016 15:16:21
%S A170214 1,13,156,1872,22464,269568,3234816,38817792,465813504,5589762048,
%T A170214 67077144576,804925734912,9659108818944,115909305827328,
%U A170214 1390911669927936,16690940039135232,200291280469622784
%N A170214 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
%C A170214 The initial terms coincide with those of A170732, although the two sequences are eventually different.
%C A170214 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170214 <a href="/index/Rec#order_40">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, -66).
%F A170214 G.f. (t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 + 2*t^33 +
%F A170214 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 +
%F A170214 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 +
%F A170214 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 +
%F A170214 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170214 1)/(66*t^40 - 11*t^39 - 11*t^38 - 11*t^37 - 11*t^36 - 11*t^35 - 11*t^34
%F A170214 - 11*t^33 - 11*t^32 - 11*t^31 - 11*t^30 - 11*t^29 - 11*t^28 - 11*t^27 -
%F A170214 11*t^26 - 11*t^25 - 11*t^24 - 11*t^23 - 11*t^22 - 11*t^21 - 11*t^20 -
%F A170214 11*t^19 - 11*t^18 - 11*t^17 - 11*t^16 - 11*t^15 - 11*t^14 - 11*t^13 -
%F A170214 11*t^12 - 11*t^11 - 11*t^10 - 11*t^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5
%F A170214 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1)
%t A170214 With[{num=Total[2t^Range[39]]+t^40+1,den=Total[-11 t^Range[39]]+ 66t^40+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jun 28 2012 *)
%K A170214 nonn
%O A170214 0,2
%A A170214 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009