cp's OEIS Frontend

A169426 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169426 #12 May 08 2018 01:03:03
%S A169426 1,29,812,22736,636608,17825024,499100672,13974818816,391294926848,
%T A169426 10956257951744,306775222648832,8589706234167296,240511774556684288,
%U A169426 6734329687587160064,188561231252440481792,5279714475068333490176
%N A169426 Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169426 The initial terms coincide with those of A170748, although the two sequences are eventually different.
%C A169426 First disagreement is at index 32, the difference is 406. - _Klaus Brockhaus_, Jun 27 2011
%C A169426 Computed with Magma using commands similar to those used to compute A154638.
%H A169426 <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, -378).
%F A169426 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)/(378*t^32 - 27*t^31 - 27*t^30 - 27*t^29 - 27*t^28 - 27*t^27 - 27*t^26 - 27*t^25 - 27*t^24 - 27*t^23 - 27*t^22 - 27*t^21 - 27*t^20 - 27*t^19 - 27*t^18 - 27*t^17 - 27*t^16 - 27*t^15 - 27*t^14 - 27*t^13 - 27*t^12 - 27*t^11 - 27*t^10 - 27*t^9 - 27*t^8 - 27*t^7 - 27*t^6 - 27*t^5 - 27*t^4 - 27*t^3 - 27*t^2 - 27*t + 1).
%F A169426 G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-27*sum(k=1..31, x^k)+378*x^32).
%Y A169426 Cf. A170748 (G.f.: (1+x)/(1-28*x) ).
%K A169426 nonn
%O A169426 0,2
%A A169426 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009