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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. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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 * A139413 A075362 A110749

Adjacent sequences:  A153122 A153123 A153124 * A153126 A153127 A153128

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Dec 20 2008

STATUS

approved

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Last modified May 20 01:04 EDT 2022. Contains 353847 sequences. (Running on oeis4.)