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A089071
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Number of liberties a big eye of size n gives in the game of Go.
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6
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1, 2, 3, 5, 8, 12, 17, 23, 30, 38, 47, 57, 68, 80, 93, 107, 122, 138, 155, 173, 192, 212, 233, 255, 278, 302, 327, 353, 380, 408, 437, 467, 498, 530, 563, 597, 632, 668, 705, 743, 782, 822, 863, 905, 948, 992, 1037, 1083, 1130, 1178, 1227, 1277, 1328, 1380
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OFFSET
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1,2
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COMMENTS
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The terms after the seventh are considered only of theoretical importance, since the largest dead shape is six spaces.
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LINKS
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Table of n, a(n) for n=1..54.
Senseis Library, Big Eye Liberties
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FORMULA
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a(n)=a(n-1)+n-2 for n>=3.
Contribution from Paul Barry, Dec 07 2009: (Start)
G.f.: (1-x+x^3)/(1-x)^3;
a(n)=n+1-0^n+C(n-1,2). (End)
a(n) = A022856(n+2). - R. J. Mathar, Oct 30 2011
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EXAMPLE
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A 5-space big eye can be almost filled in 4 moves, after which one takes and has a 4-space big eye (5 liberties) left. This gives a total of 4+5 moves for the opponent and 1 for oneself, for de facto 8 liberties.
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MATHEMATICA
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i=-1; s=3; lst={Abs[i], s+i}; Do[s+=n+i; If[s>2, AppendTo[lst, s]], {n, 0, 6!, 1}]; lst [From Vladimir Joseph Stephan Orlovsky, Oct 30 2008]
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CROSSREFS
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Sequence in context: A028955 A104664 A022856 * A177205 A175829 A175827
Adjacent sequences: A089068 A089069 A089070 * A089072 A089073 A089074
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KEYWORD
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nonn,easy
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AUTHOR
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André Engels, Dec 03 2003
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EXTENSIONS
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More terms from David Wasserman, Aug 29 2005
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STATUS
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approved
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