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
KEYWORD
nonn,easy
AUTHOR
André Engels, Dec 03 2003
EXTENSIONS
More terms from David Wasserman, Aug 29 2005
STATUS
approved