A089071 Number of liberties a big eye of size n gives in the game of Go.

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

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

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Join[{1}, Binomial[Range[65], 2] +2] (* G. C. Greubel, Oct 31 2022 *)

Prog

(Magma) [n eq 1 select 1 else Binomial(n-1, 2) +2: n in [1..65]]; // G. C. Greubel, Oct 31 2022
(SageMath) [binomial(n-1, 2)+2-int(n==1) for n in range(1, 65)] # G. C. Greubel, Oct 31 2022

Crossrefs

Cf. A022856.

Sequence in context: A338921 A333343 A022856 * A177205 A275580 A175829

Adjacent sequences: A089068 A089069 A089070 * A089072 A089073 A089074

Keyword

nonn,easy

Author

André Engels, Dec 03 2003

Extensions

More terms from David Wasserman, Aug 29 2005

Status

approved