A143976 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 == 1 (mod 3); then R(m,n) is the number of UNmarked squares in the rectangle [0,m] X [0,n].

1, 2, 2, 2, 3, 2, 3, 4, 4, 3, 4, 6, 6, 6, 4, 4, 7, 8, 8, 7, 4, 5, 8, 10, 11, 10, 8, 5, 6, 10, 12, 14, 14, 12, 10, 6, 6, 11, 14, 16, 17, 16, 14, 11, 6, 7, 12, 16, 19, 20, 20, 19, 16, 12, 7, 8, 14, 18, 22, 24, 24, 24, 22, 18, 14, 8, 8, 15, 20, 24, 27, 28, 28, 27, 24, 20, 15, 8

Offset

1,2

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) = m*n - floor(m*n/3).

Example

Northwest corner:
  1  2  2  3  4  4  5
  2  3  4  6  7  8 10
  2  4  6  8 10 12 14
  3  6  8 11 14 16 18
  4  7 10 14 17 20 24
See A143974.

Mathematica

T[m_, n_]:=m*n-Floor[m*n/3]; Flatten[Table[T[n-k+1, k], {n, 12}, {k, n}]] (* Stefano Spezia, Oct 25 2022 *)

Crossrefs

Rows: A004523, A004772, A005843, A047399, et al.

Main diagonal: A071619.

Cf. A143974, A143977, A143979.

Sequence in context: A165015 A178994 A306608 * A194296 A194336 A127159

Adjacent sequences: A143973 A143974 A143975 * A143977 A143978 A143979

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 06 2008

Status

approved