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%I #22 Nov 02 2022 07:36:24
%S 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,
%T 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,
%U 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
%N 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].
%C Rows numbered 3,6,9,12,15,... are, except for initial terms, multiples of (1,2,3,4,5,6,7,...) = A000027.
%H Stefano Spezia, <a href="/A143977/b143977.txt">First 140 antidiagonals of the array, flattened</a>
%F R(m,n) = ceiling(m*n/3). [Corrected by _Stefano Spezia_, Oct 27 2022]
%e Northwest corner:
%e 1 1 1 2 2 2 3
%e 1 2 2 3 4 4 5
%e 1 2 3 4 5 6 7
%e 2 3 4 6 7 8 10
%e 2 4 5 7 9 10 12
%t T[m_,n_]:=Ceiling[m n/3];Flatten[Table[T[m-n+1,n],{m,13},{n,m}]] (* _Stefano Spezia_, Oct 27 2022 *)
%Y Diagonals: A008810, A007984, A000212, A128422.
%Y Rows and columns: A002264, A004523, A000027, A004772, A047212, et al.
%Y Cf. A143974, A143976, A143979.
%K nonn,tabl
%O 1,5
%A _Clark Kimberling_, Sep 06 2008
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