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A103139
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Woolbright sequence: the maximum number of kings on an n X n chess board such that every single king is attacking a number of other kings that is smaller or equal to the number of empty spaces around it.
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1
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1, 2, 6, 9, 15, 22, 28, 39, 49, 59, 73
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Lower bounds for terms following 59 are as follows: 73, 86, 102, 117, 136, 153, 173, 195, 216, 239, 266, 289, 318, 345, 375, 405, 438, 471, 504, 540, 576, 614, 654, 693, 735, 777, ...
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REFERENCES
| J. E. Dunbar, D. G. Hoffman, R. C. Laskar and L. R. Markus, Alpha-domination, Discrete Mathematics, 211 (2000), pp. 11-26.
Eugen J. Ionascu, Dan Pritikin and Stephen E. Wright, k-Dependence and Domination in Kings Graphs, Amer. Math. Monthly, 115 (2008), 820-836.
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LINKS
| Eugen J. Ionascu, Dan Pritikin and Stephen E. Wright, k-Dependence and Domination in Kings Graphs
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FORMULA
| a(n)=n^2-gamma_{1/2}(n)= approx floor(3*(n^2+1)/5) (I assume this is a lower bound? - N. J. A. Sloane (njas(AT)research.att.com))
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EXAMPLE
| a(3)=6. Indeed, on a 3 X 3 chess board one can arrange six kings on two sides columns to satisfy the requirement. It is not possible to arrange seven kings since the center has to be empty and then at least one of the squares in the middle of the sides must have a king on it which requires at least three empty spaces around and that is impossible.
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CROSSREFS
| Sequence in context: A176039 A084265 A084140 * A181025 A172433 A049622
Adjacent sequences: A103136 A103137 A103138 * A103140 A103141 A103142
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KEYWORD
| nonn
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AUTHOR
| Eugen J. Ionascu (ionascu_eugen(AT)columbusstate.edu), Mar 17 2005
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EXTENSIONS
| One more term [from the Ionascu et al. paper] from Vladeta Jovovic (vladeta(AT)eunet.yu), Sep 17 2008
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