cp's OEIS Frontend

A170675 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

%I A170675 #6 Nov 21 2016 11:34:06
%S A170675 1,42,1722,70602,2894682,118681962,4865960442,199504378122,
%T A170675 8179679503002,335366859623082,13750041244546362,563751691026400842,
%U A170675 23113819332082434522,947666592615379815402,38854330297230572431482
%N A170675 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
%C A170675 The initial terms coincide with those of A170761, although the two sequences are eventually different.
%C A170675 Computed with MAGMA using commands similar to those used to compute A154638.
%H A170675 <a href="/index/Rec#order_49">Index entries for linear recurrences with constant coefficients</a>, signature (40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, -820).
%F A170675 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 A170675 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 A170675 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 A170675 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 A170675 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 A170675 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 A170675 1)/(820*t^49 - 40*t^48 - 40*t^47 - 40*t^46 - 40*t^45 - 40*t^44 - 40*t^43
%F A170675 - 40*t^42 - 40*t^41 - 40*t^40 - 40*t^39 - 40*t^38 - 40*t^37 - 40*t^36 -
%F A170675 40*t^35 - 40*t^34 - 40*t^33 - 40*t^32 - 40*t^31 - 40*t^30 - 40*t^29 -
%F A170675 40*t^28 - 40*t^27 - 40*t^26 - 40*t^25 - 40*t^24 - 40*t^23 - 40*t^22 -
%F A170675 40*t^21 - 40*t^20 - 40*t^19 - 40*t^18 - 40*t^17 - 40*t^16 - 40*t^15 -
%F A170675 40*t^14 - 40*t^13 - 40*t^12 - 40*t^11 - 40*t^10 - 40*t^9 - 40*t^8 -
%F A170675 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1)
%K A170675 nonn
%O A170675 0,2
%A A170675 _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009