cp's OEIS Frontend

A169542 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.

%I A169542 #8 Aug 08 2019 15:55:37
%S A169542 1,49,2352,112896,5419008,260112384,12485394432,599298932736,
%T A169542 28766348771328,1380784741023744,66277667569139712,
%U A169542 3181328043318706176,152703746079297896448,7329779811806299029504,351829430966702353416192
%N A169542 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
%C A169542 The initial terms coincide with those of A170768, although the two sequences are eventually different.
%C A169542 Computed with MAGMA using commands similar to those used to compute A154638.
%H A169542 <a href="/index/Rec#order_34">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, 47, 47, -1128).
%F A169542 G.f. (t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
%F A169542 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
%F A169542 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 +
%F A169542 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 +
%F A169542 2*t + 1)/(1128*t^34 - 47*t^33 - 47*t^32 - 47*t^31 - 47*t^30 - 47*t^29 -
%F A169542 47*t^28 - 47*t^27 - 47*t^26 - 47*t^25 - 47*t^24 - 47*t^23 - 47*t^22 -
%F A169542 47*t^21 - 47*t^20 - 47*t^19 - 47*t^18 - 47*t^17 - 47*t^16 - 47*t^15 -
%F A169542 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 -
%F A169542 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1)
%t A169542 coxG[{34,1128,-47}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Aug 08 2019 *)
%K A169542 nonn
%O A169542 0,2
%A A169542 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009