

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
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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 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



