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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)^4 = I.

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`%I #7 Nov 26 2016 16:29:03
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`%S 1,3,6,12,21,36,63,108,186,321,552,951,1638,2820,4857,8364,14403,
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`%T 24804,42714,73557,126672,218139,375654,646908,1114029,1918452,
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`%U 3303735,5689308,9797466,16872057,29055096,50035311,86164998,148383348
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`%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)^4 = I.
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`%C The initial terms coincide with those of A003945, although the two sequences are eventually different.
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`%C Computed with MAGMA using commands similar to those used to compute A154638.
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`%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 1, -1).
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`%F G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(t^4 - t^3 - t^2 - t + 1)
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`%K nonn
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`%O 0,2
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`%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009
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