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A143999 Rectangular array by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark squares for which (x,y) is congruent mod 4 to one of the following: (1,1), (2,3), (3,2), (4,0); then R(m,n) is the number of UNmarked squares in the rectangle [0,m]x[0,n].

%I A143999 #9 Dec 06 2017 10:56:34
%S A143999 1,1,1,1,1,1,1,2,2,1,2,2,3,2,2,2,3,3,3,3,2,2,3,4,4,4,3,2,2,4,5,5,5,5,
%T A143999 4,2,3,4,6,6,7,6,6,4,3,3,5,6,7,8,8,7,6,5,3,3,5,7,8,9,9,9,8,7,5,3,3,6,
%U A143999 8,9,10,11,11,10,9,8,6,3,4,6,9,10,12,12,13,12,12,10,9,6,4,4,7,9,11,13,14,14
%N A143999 Rectangular array by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark squares for which (x,y) is congruent mod 4 to one of the following: (1,1), (2,3), (3,2), (4,0); then R(m,n) is the number of UNmarked squares in the rectangle [0,m]x[0,n].
%C A143999 Row 4n is given by n*(1,2,3,4,5,6,...).
%H A143999 G. C. Greubel, <a href="/A143999/b143999.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F A143999 R(m,n) = m*n - floor(3*m*n/4).
%t A143999 b[n_, m_] := m*n - Floor[3*m*n/4]; a:= Table[b[n, m], {n, 1, 25}, {m, 1, 25}]; Table[a[[k, n - k + 1]], {n, 1, 20}, {k, 1, n}] // Flatten (* _G. C. Greubel_, Dec 05 2017 *)
%Y A143999 Cf. A143996, A143997, A143998, A144000, A144001.
%K A143999 nonn,tabl
%O A143999 1,8
%A A143999 _Clark Kimberling_, Sep 07 2008