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A366828
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Number of linearly independent solutions to the neighbor sum problem on a 4-dimensional chessboard of length (3n-1).
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0
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0, 4, 0, 88, 24, 4, 0, 136, 0, 220, 0, 88, 48, 52, 24, 136
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OFFSET
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1,2
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COMMENTS
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We say that a chessboard filled with integer entries satisfies the neighbor-sum property if the number appearing on each cell is the sum of entries in its neighboring cells, where neighbors are cells sharing a common edge or vertex. It has been proven in the paper by Dutta et al. that an n X n chessboard satisfies this property if and only if 6 divides (n+1). The sequence at hand deals with the analogous problem in 4 dimensions.
It has been proved that if the number of linearly independent solutions to the neighbor sum problem on a 4-dimensional chessboard of length n is nonzero, then 3 divides (n+1) -- see Theorem 28 of Dutta et al. So, the sequence at hand considers a(n) = b(3*n-1) where b(n) is the number of linearly independent solutions to the neighbor sum problem on a 4-dimensional chessboard of length n.
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LINKS
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EXAMPLE
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The case of n=2 corresponds to a 5 X 5 X 5 X 5 chessboard. Examples for the analogous problem in two dimensions are given in the paper by Dutta et al. Examples for the analogous problem in three dimensions are given in A366410.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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