cp's OEIS Frontend

A169446 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

%I A169446 #14 May 08 2018 01:09:15
%S A169446 1,49,2352,112896,5419008,260112384,12485394432,599298932736,
%T A169446 28766348771328,1380784741023744,66277667569139712,
%U A169446 3181328043318706176,152703746079297896448,7329779811806299029504,351829430966702353416192
%N A169446 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
%C A169446 The initial terms coincide with those of A170768, although the two sequences are eventually different.
%C A169446 First disagreement is at index 32, the difference is 1176. - _Klaus Brockhaus_, Jun 30 2011
%C A169446 Computed with Magma using commands similar to those used to compute A154638.
%H A169446 <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, -1128).
%F A169446 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)/(1128*t^32 - 47*t^31 - 47*t^30 - 47*t^29 - 47*t^28 - 47*t^27 - 47*t^26 - 47*t^25 - 47*t^24 - 47*t^23 - 47*t^22 - 47*t^21 - 47*t^20 - 47*t^19 - 47*t^18 - 47*t^17 - 47*t^16 - 47*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).
%F A169446 G.f.: (1+2*sum(k=1..31,x^k)+x^32)/(1-47*sum(k=1..31,x^k)+1128*x^32).
%Y A169446 Cf. A170768 (G.f.: (1+x)/(1-48*x) ).
%K A169446 nonn
%O A169446 0,2
%A A169446 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009