A143979 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].

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

Offset: 1

Author

Clark Kimberling, Sep 06 2008

Keywords

• nonn
• tabl

Comments

Rows numbered 3,6,9,12,15,... are, except for initial terms, multiples of (1,2,3,4,5,6,7,...)=A000027.

Examples

			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
		

Crossrefs

Cf. A143974, A143976, A143977.

Programs

Mathematica

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 *)

Formula

R(m,n) = m*n - ceiling(m*n/3). [Corrected by Stefano Spezia, Oct 28 2022]