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A153125 Triangle read by rows: T(n,k) = maximal number of squares that can be covered by a queen on an n X k chessboard, 1<=k<=n.

%I A153125 #8 Sep 07 2012 12:10:39
%S A153125 1,2,4,3,6,9,4,7,10,12,5,8,11,14,17,6,9,12,15,18,20,7,10,13,16,19,22,
%T A153125 25,8,11,14,17,20,23,26,28,9,12,15,18,21,24,27,30,33,10,13,16,19,22,
%U A153125 25,28,31,34,36,11,14,17,20,23,26,29,32,35,38,41,12,15,18,21,24,27,30,33,36
%N A153125 Triangle read by rows: T(n,k) = maximal number of squares that can be covered by a queen on an n X k chessboard, 1<=k<=n.
%C A153125 Sums of rows give A153126; central terms give A016861;
%C A153125 A047461(n) = T(n,n);
%C A153125 T(n,2*k-1) = T(n-1,2*k-1) + 1 for 2*k-1<n.
%F A153125 T(n,k) = n + 3*(k-1) - (1 - n Mod 2)*delta_{n,k}, 1<=k<=n; delta is the Kronecker symbol.
%e A153125 Triangle T(n,k) begins:
%e A153125 1;
%e A153125 2,  4;
%e A153125 3,  6,  9;
%e A153125 4,  7, 10, 12;
%e A153125 5,  8, 11, 14, 17;
%e A153125 6,  9, 12, 15, 18, 20;
%e A153125 7, 10, 13, 16, 19, 22, 25;
%e A153125 8, 11, 14, 17, 20, 23, 26, 28;
%t A153125 T[n_,k_]:=n+3*(k-1)-(1-Mod[n,2])*If[k==n,1,0];
%t A153125 Flatten[Table[Table[T[n,k],{k,1,n}],{n,1,20}]]
%t A153125 (* From _Vaclav Kotesovec_, Sep 07 2012 *)
%K A153125 nonn,tabl
%O A153125 1,2
%A A153125 _Reinhard Zumkeller_, Dec 20 2008