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A143979
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Rectangular array R by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark squares having |x-y| = 0 (mod 3); then R(m,n) is the number of UNmarked squares in the rectangle [0,m] X [0,n].
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5
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0, 1, 1, 2, 2, 2, 2, 4, 4, 2, 3, 5, 6, 5, 3, 4, 6, 8, 8, 6, 4, 4, 8, 10, 10, 10, 8, 4, 5, 9, 12, 13, 13, 12, 9, 5, 6, 10, 14, 16, 16, 16, 14, 10, 6, 6, 12, 16, 18, 20, 20, 18, 16, 12, 6, 7, 13, 18, 21, 23, 24, 23, 21, 18, 13, 7, 8, 14, 20, 24, 26, 28, 28, 26, 24, 20, 14, 8
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OFFSET
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1,4
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COMMENTS
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Rows numbered 3,6,9,12,15,... are, except for initial terms, multiples of (1,2,3,4,5,6,7,...)=A000027.
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LINKS
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FORMULA
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R(m,n) = m*n - ceiling(m*n/3). [Corrected by Stefano Spezia, Oct 28 2022]
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EXAMPLE
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Northwest corner:
0 1 2 2 3 4 4
1 2 4 5 6 8 9
2 4 6 8 10 12 14
2 5 8 10 13 16 18
3 6 10 13 16 20 23
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MATHEMATICA
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T[i_, j_]:=i*j-Ceiling[i*j/3]; Flatten[Table[T[m-n+1, n], {m, 12}, {n, m}]] (* Stefano Spezia, Oct 28 2022 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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