cp's OEIS Frontend

A170656 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

%I A170656 #9 Nov 21 2016 11:23:06
%S A170656 1,23,506,11132,244904,5387888,118533536,2607737792,57370231424,
%T A170656 1262145091328,27767192009216,610878224202752,13439320932460544,
%U A170656 295665060514131968,6504631331310903296,143101889288839872512
%N A170656 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
%C A170656 The initial terms coincide with those of A170742, although the two sequences are eventually different.
%C A170656 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170656 <a href="/index/Rec#order_49">Index entries for linear recurrences with constant coefficients</a>, signature (21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -231).
%F A170656 G.f. (t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 +
%F A170656 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170656 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A170656 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A170656 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A170656 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +
%F A170656 1)/(231*t^49 - 21*t^48 - 21*t^47 - 21*t^46 - 21*t^45 - 21*t^44 - 21*t^43
%F A170656 - 21*t^42 - 21*t^41 - 21*t^40 - 21*t^39 - 21*t^38 - 21*t^37 - 21*t^36 -
%F A170656 21*t^35 - 21*t^34 - 21*t^33 - 21*t^32 - 21*t^31 - 21*t^30 - 21*t^29 -
%F A170656 21*t^28 - 21*t^27 - 21*t^26 - 21*t^25 - 21*t^24 - 21*t^23 - 21*t^22 -
%F A170656 21*t^21 - 21*t^20 - 21*t^19 - 21*t^18 - 21*t^17 - 21*t^16 - 21*t^15 -
%F A170656 21*t^14 - 21*t^13 - 21*t^12 - 21*t^11 - 21*t^10 - 21*t^9 - 21*t^8 -
%F A170656 21*t^7 - 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1)
%t A170656 With[{num=Total[2t^Range[48]]+t^49+1,den=Total[-21 t^Range[48]]+ 231t^49+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* _Harvey P. Dale_, Jul 12 2011 *)
%K A170656 nonn
%O A170656 0,2
%A A170656 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009