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A168777
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Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.
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0
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1, 4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78732, 236196, 708588, 2125764, 6377292, 19131876, 57395628, 172186884, 516560652, 1549681950, 4649045832, 13947137448, 41841412200, 125524236168, 376572707208, 1129718117736
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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 A003946, although the two sequences are eventually different.
First disagreement at index 19: a(19) = 1549681950, A003946(19) = 1549681956.
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..25.
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FORMULA
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G.f.: (t^19 + 2*t^18 + 2*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)/(3*t^19 - 2*t^18 - 2*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).
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CROSSREFS
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Cf. A003946 (G.f.: (1+x)/(1-3*x)).
Sequence in context: A167882 A168681 A168729 * A168825 A168873 A168921
Adjacent sequences: A168774 A168775 A168776 * A168778 A168779 A168780
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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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