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A170683 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I. 0

%I

%S 1,50,2450,120050,5882450,288240050,14123762450,692064360050,

%T 33911153642450,1661646528480050,81420679895522450,

%U 3989613314880600050,195491052429149402450,9579061569028320720050,469374016882387715282450

%N Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

%C The initial terms coincide with those of A170769, although the two sequences are eventually different.

%C Computed with MAGMA using commands similar to those used to compute A154638.

%H <a href="/index/Rec#order_49">Index entries for linear recurrences with constant coefficients</a>, signature (48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, -1176).

%F 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 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 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 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 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 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 1)/(1176*t^49 - 48*t^48 - 48*t^47 - 48*t^46 - 48*t^45 - 48*t^44 -

%F 48*t^43 - 48*t^42 - 48*t^41 - 48*t^40 - 48*t^39 - 48*t^38 - 48*t^37 -

%F 48*t^36 - 48*t^35 - 48*t^34 - 48*t^33 - 48*t^32 - 48*t^31 - 48*t^30 -

%F 48*t^29 - 48*t^28 - 48*t^27 - 48*t^26 - 48*t^25 - 48*t^24 - 48*t^23 -

%F 48*t^22 - 48*t^21 - 48*t^20 - 48*t^19 - 48*t^18 - 48*t^17 - 48*t^16 -

%F 48*t^15 - 48*t^14 - 48*t^13 - 48*t^12 - 48*t^11 - 48*t^10 - 48*t^9 -

%F 48*t^8 - 48*t^7 - 48*t^6 - 48*t^5 - 48*t^4 - 48*t^3 - 48*t^2 - 48*t + 1)

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009

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Last modified June 24 14:24 EDT 2021. Contains 345417 sequences. (Running on oeis4.)