cp's OEIS Frontend

A169425 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169425 #12 May 08 2018 01:01:21
%S A169425 1,28,756,20412,551124,14880348,401769396,10847773692,292889889684,
%T A169425 7908027021468,213516729579636,5764951698650172,155653695863554644,
%U A169425 4202649788315975388,113471544284531335476,3063731695682346057852
%N A169425 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169425 The initial terms coincide with those of A170747, although the two sequences are eventually different.
%C A169425 First disagreement is at index 32, the difference is 378. - _Klaus Brockhaus_, Jun 27 2011
%C A169425 Computed with Magma using commands similar to those used to compute A154638.
%H A169425 <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, -351).
%F A169425 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)/(351*t^32 - 26*t^31 - 26*t^30 - 26*t^29 - 26*t^28 - 26*t^27 - 26*t^26 - 26*t^25 - 26*t^24 - 26*t^23 - 26*t^22 - 26*t^21 - 26*t^20 - 26*t^19 - 26*t^18 - 26*t^17 - 26*t^16 - 26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).
%F A169425 G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-26*sum(k=1..31, x^k)+351*x^32).
%Y A169425 Cf. A170747 (G.f.: (1+x)/(1-27*x) ).
%K A169425 nonn
%O A169425 0,2
%A A169425 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009