A143974 Rectangular array R by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark those having x+y=1(mod 3); then R(m,n) is the number of marked unit squares in the rectangle [0,m]x[0,n].

0, 0, 0, 1, 1, 1, 1, 2, 2, 1, 1, 2, 3, 2, 1, 2, 3, 4, 4, 3, 2, 2, 4, 5, 5, 5, 4, 2, 2, 4, 6, 6, 6, 6, 4, 2, 3, 5, 7, 8, 8, 8, 7, 5, 3, 3, 6, 8, 9, 10, 10, 9, 8, 6, 3, 3, 6, 9, 10, 11, 12, 11, 10, 9, 6, 3, 4, 7, 10, 12, 13, 14, 14, 13, 12, 10, 7, 4, 4, 8, 11, 13, 15, 16, 16, 16, 15, 13, 11, 8, 4, 4, 8

Offset

1,8

Comments

Diagonals: A000212, A128422, A032765, A143975, A071408.

Rows: A002264, A004523, A000027, A004773, A138235, A005843, A047349 et al.

Links

Table of n, a(n) for n=1..93.

Formula

R(m,n)=floor(mn/3).

Example

Northwest corner:
0 0 1 1 1 2
0 1 2 2 3 4
1 2 3 4 5 6
1 2 4 5 6 8
1 3 5 6 8 10
R(3,4) counts these marked squares: (1,3), (2,2), (3,1), (3,4).

Crossrefs

Cf. A143976, A143977.

Sequence in context: A275420 A344961 A343853 * A301565 A237265 A035463

Adjacent sequences: A143971 A143972 A143973 * A143975 A143976 A143977

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 06 2008

Status

approved