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 A089071 Number of liberties a big eye of size n gives in the game of Go. 11
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The terms after the seventh are considered to be of only theoretical importance, since the largest dead shape is six spaces. LINKS Senseis Library, Big Eye Liberties Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = a(n-1) + n - 2 for n>=3. 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 EXAMPLE 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. MATHEMATICA i=-1; s=3; lst={Abs[i], s+i}; Do[s+=n+i; If[s>2, AppendTo[lst, s]], {n, 0, 6!, 1}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 30 2008 *) CROSSREFS Sequence in context: A246321 A104664 A022856 * A177205 A275580 A175829 Adjacent sequences:  A089068 A089069 A089070 * A089072 A089073 A089074 KEYWORD nonn,easy AUTHOR AndrĂ© Engels, Dec 03 2003 EXTENSIONS More terms from David Wasserman, Aug 29 2005 STATUS approved

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Last modified July 19 08:23 EDT 2019. Contains 325155 sequences. (Running on oeis4.)