A143999 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: (1,1), (2,3), (3,2), (4,0); then R(m,n) is the number of UNmarked squares in the rectangle [0,m]x[0,n].

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 3, 2, 2, 2, 3, 3, 3, 3, 2, 2, 3, 4, 4, 4, 3, 2, 2, 4, 5, 5, 5, 5, 4, 2, 3, 4, 6, 6, 7, 6, 6, 4, 3, 3, 5, 6, 7, 8, 8, 7, 6, 5, 3, 3, 5, 7, 8, 9, 9, 9, 8, 7, 5, 3, 3, 6, 8, 9, 10, 11, 11, 10, 9, 8, 6, 3, 4, 6, 9, 10, 12, 12, 13, 12, 12, 10, 9, 6, 4, 4, 7, 9, 11, 13, 14, 14

Offset

1,8

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

Formula

R(m,n) = m*n - floor(3*m*n/4).

Mathematica

b[n_, m_] := m*n - Floor[3*m*n/4]; a:= Table[b[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 *)

Crossrefs

Cf. A143996, A143997, A143998, A144000, A144001.

Sequence in context: A050333 A343189 A271775 * A137419 A057536 A245574

Adjacent sequences: A143996 A143997 A143998 * A144000 A144001 A144002

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 07 2008

Status

approved