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A089071
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Number of liberties a big eye of size n gives in the game of Go.
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14
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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
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1,2
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COMMENTS
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The terms after the seventh are considered to be of only theoretical importance, since the largest dead shape is six spaces.
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LINKS
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FORMULA
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a(n) = a(n-1) + n - 2 for n>=3.
G.f.: (1 - x + x^3)/(1-x)^3.
a(n) = n + 1 - 0^n + C(n-1,2). (End)
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EXAMPLE
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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.
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MATHEMATICA
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Join[{1}, Binomial[Range[65], 2] +2] (* G. C. Greubel, Oct 31 2022 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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