cp's OEIS Frontend

A169429 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169429 #11 May 08 2018 01:04:24
%S A169429 1,32,992,30752,953312,29552672,916132832,28400117792,880403651552,
%T A169429 27292513198112,846067909141472,26228105183385632,813071260684954592,
%U A169429 25205209081233592352,781361481518241362912,24222205927065482250272
%N A169429 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169429 The initial terms coincide with those of A170751, although the two sequences are eventually different.
%C A169429 First disagreement is at index 32, the difference is 496. - _Klaus Brockhaus_, Jun 30 2011
%C A169429 Computed with Magma using commands similar to those used to compute A154638.
%H A169429 <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, -465).
%F A169429 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)/(465*t^32 - 30*t^31 - 30*t^30 - 30*t^29 - 30*t^28 - 30*t^27 - 30*t^26 - 30*t^25 - 30*t^24 - 30*t^23 - 30*t^22 - 30*t^21 - 30*t^20 - 30*t^19 - 30*t^18 - 30*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).
%F A169429 G.f.: (1+2*sum(k=1..31,x^k)+x^32)/(1-30*sum(k=1..31,x^k)+465*x^32).
%Y A169429 Cf. A170751 (G.f.: (1+x)/(1-31*x) ).
%K A169429 nonn
%O A169429 0,2
%A A169429 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009