cp's OEIS Frontend

A169415 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169415 #12 May 08 2018 00:56:56
%S A169415 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,
%T A169415 125563633938,2134581776946,36287890208082,616894133537394,
%U A169415 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274
%N A169415 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169415 The initial terms coincide with those of A170737, although the two sequences are eventually different.
%C A169415 First disagreement is at index 32, the difference is 153. - _Klaus Brockhaus_, Jun 27 2011
%C A169415 Computed with Magma using commands similar to those used to compute A154638.
%H A169415 <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, -136).
%F A169415 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)/(136*t^32 - 16*t^31 - 16*t^30 - 16*t^29 - 16*t^28 - 16*t^27 - 16*t^26 - 16*t^25 - 16*t^24 - 16*t^23 - 16*t^22 - 16*t^21 - 16*t^20 - 16*t^19 - 16*t^18 - 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).
%F A169415 G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-16*sum(k=1..31, x^k)+136*x^32).
%Y A169415 Cf. A170737 (G.f.: (1+x)/(1-17*x) ).
%K A169415 nonn
%O A169415 0,2
%A A169415 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009