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A168682
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Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.
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0
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1, 5, 20, 80, 320, 1280, 5120, 20480, 81920, 327680, 1310720, 5242880, 20971520, 83886080, 335544320, 1342177280, 5368709120, 21474836470, 85899345840, 343597383210, 1374389532240, 5497558126560, 21990232496640, 87960929948160
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OFFSET
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0,2
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COMMENTS
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The initial terms coincide with those of A003947, although the two sequences are eventually different.
First disagreement at index 17: a(17) = 21474836470, A003947(17) = 21474836480. - Klaus Brockhaus, Mar 30 2011
Computed with MAGMA using commands similar to those used to compute A154638.
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LINKS
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Table of n, a(n) for n=0..23.
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FORMULA
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G.f.: (t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 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 + 1)/(6*t^17 - 3*t^16 - 3*t^15 - 3*t^14 - 3*t^13 - 3*t^12 - 3*t^11 - 3*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1).
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CROSSREFS
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Cf. A003947 (G.f.: (1+x)/(1-4*x)).
Sequence in context: A167106 A167650 A167896 * A168730 A168778 A168826
Adjacent sequences: A168679 A168680 A168681 * A168683 A168684 A168685
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KEYWORD
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nonn
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AUTHOR
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John Cannon (john(AT)maths.usyd.edu.au) and N. J. A. Sloane, Dec 03 2009
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STATUS
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approved
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