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Rectangular array R by antidiagonals: R(m,n) = number of black squares
1

%I #2 Mar 30 2012 18:57:10

%S 0,1,1,1,2,1,2,3,3,2,2,4,4,4,2,3,5,6,6,5,3,3,6,7,8,7,6,3,4,7,9,10,10,

%T 9,7,4,4,8,10,12,12,12,10,8,4,5,9,12,14,15,15,14,12,9,5,5,10,13,16,17,

%U 18,17,16,13,10,5,6,11,15,18,20,21,21,20,18,15,11,6,6,12,16,20,22

%N Rectangular array R by antidiagonals: R(m,n) = number of black squares

%C Antidiagonal sums: (2,4,10,16,28,40,60,80,...)=A006584 (conjectured).

%C Diagonals: A007590, A000217.

%F R(m,n)=Floor(mn/2).

%e Northwest corner:

%e 0 1 1 2 2 3 3 4

%e 1 2 3 4 5 6 7 8

%e 1 3 4 6 7 9 10 12

%e 2 4 6 8 10 12 14 16

%Y Cf. A143901.

%K nonn,tabl

%O 1,5

%A _Clark Kimberling_, Sep 04 2008