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A278290
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Number of neighbors of each new term in a square array read by antidiagonals.
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4
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0, 1, 2, 1, 4, 2, 1, 4, 4, 2, 1, 4, 4, 4, 2, 1, 4, 4, 4, 4, 2, 1, 4, 4, 4, 4, 4, 2, 1, 4, 4, 4, 4, 4, 4, 2, 1, 4, 4, 4, 4, 4, 4, 4, 2, 1, 4, 4, 4, 4, 4, 4, 4, 4, 2, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2
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OFFSET
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1,3
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COMMENTS
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Here the "neighbors" of T(n,k) are defined to be the adjacent elements to T(n,k), in the same row, column or diagonals, that are present in the square array when T(n,k) is the new element of the sequence in progress.
Apart from row 1 and column 1 the rest of the elements are 4's.
If every "4" is replaced with a "3" we have the sequence A275015.
For the same idea but for a right triangle see A278317; for an isosceles triangle see A275015; for a square spiral see A278354; and for a hexagonal spiral see A047931.
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LINKS
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EXAMPLE
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The corner of the square array read by antidiagonals upwards begins:
0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,...
1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,...
1, 4, 4, 4, 4, 4, 4, 4, 4, 4,...
1, 4, 4, 4, 4, 4, 4, 4, 4,...
1, 4, 4, 4, 4, 4, 4, 4,...
1, 4, 4, 4, 4, 4, 4,...
1, 4, 4, 4, 4, 4,...
1, 4, 4, 4, 4,...
1, 4, 4, 4,...
1, 4, 4,...
1, 4,...
1,...
..
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MATHEMATICA
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Table[Boole[# > 1] + 2 Boole[k > 1] + Boole[And[# > 1, k > 1]] &[n - k + 1], {n, 14}, {k, n}] // Flatten (* or *)
Table[Boole[n > 1] (Map[Mod[#, n] &, Range@ n] /. {k_ /; k > 1 -> 4, 0 -> 2}), {n, 14}] // Flatten (* Michael De Vlieger, Nov 23 2016 *)
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CROSSREFS
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Antidiagonal sums give 0 together with A004767.
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KEYWORD
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AUTHOR
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STATUS
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approved
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