cp's OEIS Frontend

A169408 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169408 #15 Nov 25 2018 18:01:56
%S A169408 1,11,110,1100,11000,110000,1100000,11000000,110000000,1100000000,
%T A169408 11000000000,110000000000,1100000000000,11000000000000,
%U A169408 110000000000000,1100000000000000,11000000000000000,110000000000000000
%N A169408 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169408 The initial terms coincide with those of A003953, although the two sequences are eventually different.
%C A169408 First disagreement is at index 32, the difference is 55. - _Klaus Brockhaus_, Jun 27 2011
%C A169408 Computed with Magma using commands similar to those used to compute A154638.
%H A169408 <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -45).
%F A169408 G.f.: (t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 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 + 2*t^2 + 2*t + 1)/(45*t^32 - 9*t^31 - 9*t^30 - 9*t^29 - 9*t^28 - 9*t^27 - 9*t^26 - 9*t^25 - 9*t^24 - 9*t^23 - 9*t^22 - 9*t^21 - 9*t^20 - 9*t^19 - 9*t^18 - 9*t^17 - 9*t^16 - 9*t^15 - 9*t^14 - 9*t^13 - 9*t^12 - 9*t^11 - 9*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).
%F A169408 G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-9*sum(k=1..31, x^k)+45*x^32).
%t A169408 coxG[{32,45,-9}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Nov 25 2018 *)
%Y A169408 Cf. A003953 (G.f.: (1+x)/(1-10*x) ).
%K A169408 nonn
%O A169408 0,2
%A A169408 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009