cp's OEIS Frontend

A170682 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

%I A170682 #8 Sep 05 2023 18:27:31
%S A170682 1,49,2352,112896,5419008,260112384,12485394432,599298932736,
%T A170682 28766348771328,1380784741023744,66277667569139712,
%U A170682 3181328043318706176,152703746079297896448,7329779811806299029504,351829430966702353416192
%N A170682 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
%C A170682 The initial terms coincide with those of A170768, although the two sequences are eventually different.
%C A170682 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170682 <a href="/index/Rec#order_49">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, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, -1128).
%F A170682 G.f. (t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 +
%F A170682 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 + 2*t^34 +
%F A170682 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 +
%F A170682 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 +
%F A170682 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 +
%F A170682 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 +
%F A170682 1)/(1128*t^49 - 47*t^48 - 47*t^47 - 47*t^46 - 47*t^45 - 47*t^44 -
%F A170682 47*t^43 - 47*t^42 - 47*t^41 - 47*t^40 - 47*t^39 - 47*t^38 - 47*t^37 -
%F A170682 47*t^36 - 47*t^35 - 47*t^34 - 47*t^33 - 47*t^32 - 47*t^31 - 47*t^30 -
%F A170682 47*t^29 - 47*t^28 - 47*t^27 - 47*t^26 - 47*t^25 - 47*t^24 - 47*t^23 -
%F A170682 47*t^22 - 47*t^21 - 47*t^20 - 47*t^19 - 47*t^18 - 47*t^17 - 47*t^16 -
%F A170682 47*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 -
%F A170682 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1)
%t A170682 coxG[{49,1128,-47}] (* The coxG program is at A169452 *)  (* _Harvey P. Dale_, Sep 05 2023 *)
%K A170682 nonn
%O A170682 0,2
%A A170682 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009