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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].

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