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A143996
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Rectangular array by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark squares for which (x,y) is congruent mod 4 to one of the following: (1,4), (2,2), (3,3), (4,1); then R(m,n) is the number of marked squares in the rectangle [0,m]x[0,n].
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6
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0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 3, 3, 2, 1, 1, 3, 3, 4, 3, 3, 1, 2, 3, 4, 5, 5, 4, 3, 2, 2, 4, 5, 6, 6, 6, 5, 4, 2, 2, 4, 6, 7, 7, 7, 7, 6, 4, 2, 2, 5, 6, 8, 8, 9, 8, 8, 6, 5, 2, 3, 5, 7, 9, 10, 10, 10, 10, 9, 7, 5, 3, 3, 6, 8, 10, 11, 12, 12, 12, 11, 10, 8, 6, 3, 3, 6, 9, 11, 12, 13, 14
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OFFSET
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1,12
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COMMENTS
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Row 4n is given by n*(1,2,3,4,5,6,...).
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LINKS
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FORMULA
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R(m,n) = floor(m*n/4).
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MATHEMATICA
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b[n_, m_] := Floor[m*n/4]; a:= Table[a[n, m], {n, 1, 25}, {m, 1, 25}]; Table[a[[k, n - k + 1]], {n, 1, 20}, {k, 1, n}] // Flatten (* G. C. Greubel, Dec 05 2017 *)
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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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