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Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
0

%I #6 Nov 21 2016 10:56:50

%S 1,3,6,12,24,48,96,192,384,768,1536,3072,6144,12288,24576,49152,98304,

%T 196608,393216,786432,1572864,3145728,6291456,12582912,25165824,

%U 50331648,100663296,201326592,402653184,805306368,1610612736,3221225472

%N Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

%C The initial terms coincide with those of A003945, 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_48">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1).

%F G.f. (t^48 + t^47 + t^46 + t^45 + t^44 + t^43 + t^42 + t^41 + t^40 + t^39 + t^38

%F + t^37 + t^36 + t^35 + t^34 + t^33 + t^32 + t^31 + t^30 + t^29 + t^28 +

%F t^27 + t^26 + t^25 + t^24 + t^23 + t^22 + t^21 + t^20 + t^19 + t^18 +

%F t^17 + t^16 + t^15 + t^14 + t^13 + t^12 + t^11 + t^10 + t^9 + t^8 + t^7

%F + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1)/(t^48 - 2*t^47 + t^46 - 2*t^45 +

%F t^44 - 2*t^43 + t^42 - 2*t^41 + t^40 - 2*t^39 + t^38 - 2*t^37 + t^36 -

%F 2*t^35 + t^34 - 2*t^33 + t^32 - 2*t^31 + t^30 - 2*t^29 + t^28 - 2*t^27 +

%F t^26 - 2*t^25 + t^24 - 2*t^23 + t^22 - 2*t^21 + t^20 - 2*t^19 + t^18 -

%F 2*t^17 + t^16 - 2*t^15 + t^14 - 2*t^13 + t^12 - 2*t^11 + t^10 - 2*t^9 +

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

%K nonn

%O 0,2

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