cp's OEIS Frontend

A143979 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 UNmarked squares in the rectangle [0,m] X [0,n].

%I A143979 #10 Oct 28 2022 15:11:22
%S A143979 0,1,1,2,2,2,2,4,4,2,3,5,6,5,3,4,6,8,8,6,4,4,8,10,10,10,8,4,5,9,12,13,
%T A143979 13,12,9,5,6,10,14,16,16,16,14,10,6,6,12,16,18,20,20,18,16,12,6,7,13,
%U A143979 18,21,23,24,23,21,18,13,7,8,14,20,24,26,28,28,26,24,20,14,8
%N A143979 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 UNmarked squares in the rectangle [0,m] X [0,n].
%C A143979 Rows numbered 3,6,9,12,15,... are, except for initial terms, multiples of (1,2,3,4,5,6,7,...)=A000027.
%F A143979 R(m,n) = m*n - ceiling(m*n/3). [Corrected by _Stefano Spezia_, Oct 28 2022]
%e A143979 Northwest corner:
%e A143979   0 1  2  2  3  4  4
%e A143979   1 2  4  5  6  8  9
%e A143979   2 4  6  8 10 12 14
%e A143979   2 5  8 10 13 16 18
%e A143979   3 6 10 13 16 20 23
%t A143979 T[i_,j_]:=i*j-Ceiling[i*j/3]; Flatten[Table[T[m-n+1,n],{m,12},{n,m}]] (* _Stefano Spezia_, Oct 28 2022 *)
%Y A143979 Cf. A143974, A143976, A143977.
%K A143979 nonn,tabl
%O A143979 1,4
%A A143979 _Clark Kimberling_, Sep 06 2008