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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].
7
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.
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.
Sequence in context: A165015 A178994 A306608 * A194296 A194336 A127159
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Sep 06 2008
STATUS
approved