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.

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, 25, 8, 11, 14, 17, 20, 23, 26, 28, 9, 12, 15, 18, 21, 24, 27, 30, 33, 10, 13, 16, 19, 22, 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

Offset

1,2

Comments

Sums of rows give A153126; central terms give A016861;

A047461(n) = T(n,n);

T(n,2*k-1) = T(n-1,2*k-1) + 1 for 2*k-1<n.

Links

Table of n, a(n) for n=1..75.

Formula

T(n,k) = n + 3*(k-1) - (1 - n Mod 2)*delta_{n,k}, 1<=k<=n; delta is the Kronecker symbol.

Example

Triangle T(n,k) begins:
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, 25;
8, 11, 14, 17, 20, 23, 26, 28;

Mathematica

T[n_, k_]:=n+3*(k-1)-(1-Mod[n, 2])*If[k==n, 1, 0];
Flatten[Table[Table[T[n, k], {k, 1, n}], {n, 1, 20}]]
(* From Vaclav Kotesovec, Sep 07 2012 *)

Crossrefs

Sequence in context: A212485 A077661 A077583 * A359697 A139413 A075362

Adjacent sequences: A153122 A153123 A153124 * A153126 A153127 A153128

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Dec 20 2008

Status

approved