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A287392
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Domination number for lion's graph on an n X n board.
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1
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0, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 9, 9, 9, 9, 9, 16, 16, 16, 16, 16, 25, 25, 25, 25, 25, 36, 36, 36, 36, 36, 49, 49, 49, 49, 49, 64, 64, 64, 64, 64, 81, 81, 81, 81, 81, 100, 100, 100, 100, 100, 121, 121, 121, 121, 121, 144, 144, 144, 144, 144, 169, 169, 169
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OFFSET
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0,7
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COMMENTS
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Minimum number of lions (from Chu shogi, Dai shogi and other Shogi variants) required to dominate an n X n board.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,2,-2,0,0,0,-1,1).
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FORMULA
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a(n) = floor((n+4)/5)^2.
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EXAMPLE
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For n=6 we need a(6)=4 lions to dominate a 6 X 6 board.
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MATHEMATICA
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Table[Floor[(i+4)/5]^2, {i, 0, 64}]
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PROG
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(Python) [int((n+4)/5)**2 for n in range(64)]
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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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STATUS
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approved
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