A143998 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 marked squares in the rectangle [0,m]x[0,n].

0, 1, 1, 2, 3, 2, 3, 4, 4, 3, 3, 6, 6, 6, 3, 4, 7, 9, 9, 7, 4, 5, 9, 11, 12, 11, 9, 5, 6, 10, 13, 15, 15, 13, 10, 6, 6, 12, 15, 18, 18, 18, 15, 12, 6, 7, 13, 18, 21, 22, 22, 21, 18, 13, 7, 8, 15, 20, 24, 26, 27, 26, 24, 20, 15, 8, 9, 16, 22, 27, 30, 31, 31, 30, 27, 22, 16, 9, 9, 18, 24, 30

Offset

1,4

Comments

Row 4n is given by 3n*(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) = floor(3*m*n/4).

Mathematica

b[n_, m_] := Floor[3*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 *)

Crossrefs

Cf. A143996, A143997, A143999, A144000, A144001.

Sequence in context: A124525 A106788 A123175 * A054237 A360495 A129600

Adjacent sequences: A143995 A143996 A143997 * A143999 A144000 A144001

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 07 2008

Status

approved