A143977 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 marked squares in the rectangle [0,m] X [0,n].

1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 3, 3, 2, 2, 4, 4, 4, 4, 2, 3, 4, 5, 6, 5, 4, 3, 3, 5, 6, 7, 7, 6, 5, 3, 3, 6, 7, 8, 9, 8, 7, 6, 3, 4, 6, 8, 10, 10, 10, 10, 8, 6, 4, 4, 7, 9, 11, 12, 12, 12, 11, 9, 7, 4, 4, 8, 10, 12, 14, 14, 14, 14, 12, 10, 8, 4, 5, 8, 11, 14, 15, 16, 17, 16, 15, 14, 11, 8, 5

Offset

1,5

Comments

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

Links

Stefano Spezia, First 140 antidiagonals of the array, flattened

Formula

R(m,n) = ceiling(m*n/3). [Corrected by Stefano Spezia, Oct 27 2022]

Example

Northwest corner:
  1  1  1  2  2  2  3
  1  2  2  3  4  4  5
  1  2  3  4  5  6  7
  2  3  4  6  7  8 10
  2  4  5  7  9 10 12

Mathematica

T[m_, n_]:=Ceiling[m n/3]; Flatten[Table[T[m-n+1, n], {m, 13}, {n, m}]] (* Stefano Spezia, Oct 27 2022 *)

Crossrefs

Diagonals: A008810, A007984, A000212, A128422.

Rows and columns: A002264, A004523, A000027, A004772, A047212, et al.

Cf. A143974, A143976, A143979.

Sequence in context: A024937 A378126 A350823 * A115265 A105223 A025859

Adjacent sequences: A143974 A143975 A143976 * A143978 A143979 A143980

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 06 2008

Status

approved