A143997 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 UNmarked squares in the rectangle [0,m]x[0,n].

1, 2, 2, 3, 3, 3, 3, 5, 5, 3, 4, 6, 7, 6, 4, 5, 8, 9, 9, 8, 5, 6, 9, 12, 12, 12, 9, 6, 6, 11, 14, 15, 15, 14, 11, 6, 7, 12, 16, 18, 19, 18, 16, 12, 7, 8, 14, 18, 21, 23, 23, 21, 18, 14, 8, 9, 15, 21, 24, 27, 27, 27, 24, 21, 15, 9, 9, 17, 23, 27, 30, 32, 32, 30, 27, 23, 17, 9, 10, 18, 25

Offset: 1

Author

Clark Kimberling, Sep 07 2008

Keywords

• nonn
• tabl

Comments

Row 4n is given by n*(1,2,3,4,5,6,...).

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Crossrefs

Cf. A143996, A143998, A143999, A144000, A144001.

Programs

Mathematica

b[n_, m_] := m*n - Floor[m*n/4]; a:= Table[a[n, m], {n, 1, 25}, {m, 1, 25}]; Table[b[[k, n - k + 1]], {n, 1, 20}, {k, 1, n}] // Flatten (* G. C. Greubel, Dec 05 2017 *)

Formula

R(m,n) = m*n - floor(m*n/4).