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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].

%I A143976 #25 Nov 02 2022 07:35:54
%S A143976 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,
%T A143976 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,
%U A143976 14,18,22,24,24,24,22,18,14,8,8,15,20,24,27,28,28,27,24,20,15,8
%N 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].
%C A143976 Rows numbered 3,6,9,12,15,... are, except for initial terms, multiples of (1,2,3,4,5,6,7,...) = A000027.
%H A143976 Stefano Spezia, <a href="/A143976/b143976.txt">First 140 antidiagonals of the array, flattened</a>
%F A143976 R(m,n) = m*n - floor(m*n/3).
%e A143976 Northwest corner:
%e A143976   1  2  2  3  4  4  5
%e A143976   2  3  4  6  7  8 10
%e A143976   2  4  6  8 10 12 14
%e A143976   3  6  8 11 14 16 18
%e A143976   4  7 10 14 17 20 24
%e A143976 See A143974.
%t A143976 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 *)
%Y A143976 Rows: A004523, A004772, A005843, A047399, et al.
%Y A143976 Main diagonal: A071619.
%Y A143976 Cf. A143974, A143977, A143979.
%K A143976 nonn,tabl
%O A143976 1,2
%A A143976 _Clark Kimberling_, Sep 06 2008