

A089071


Number of liberties a big eye of size n gives in the game of Go.


9



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

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

Table of n, a(n) for n=1..54.
Senseis Library, Big Eye Liberties
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

a(n) = a(n1) + n  2 for n>=3.
From Paul Barry, Dec 07 2009: (Start)
G.f.: (1  x + x^3)/(1x)^3;
a(n) = n + 1  0^n + C(n1,2). (End)
a(n) = A022856(n+2).  R. J. Mathar, Oct 30 2011


EXAMPLE

A 5space big eye can be almost filled in 4 moves, after which one takes and has a 4space 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 A175829 A241552
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



