A063712 Table of bits required for product of n- and k-bit positive numbers read by antidiagonals.

1, 2, 2, 3, 4, 3, 4, 5, 5, 4, 5, 6, 6, 6, 5, 6, 7, 7, 7, 7, 6, 7, 8, 8, 8, 8, 8, 7, 8, 9, 9, 9, 9, 9, 9, 8, 9, 10, 10, 10, 10, 10, 10, 10, 9, 10, 11, 11, 11, 11, 11, 11, 11, 11, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 11, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 13, 14, 14

Offset

1,2

Comments

This sequence is A063711 without zeros.

The first entry is a(1,1) which (arbitrarily) is considered to have offset 1.

a(n, k) is also the maximal number of rooks that can be placed on an n X k chessboard so that each rook is attacked by at most (equivalently, exactly) two others. (If more than two rooks lie in a given row or column, each rook attacks only its nearest neighbors. That is, rooks don't jump.) - Joel B. Lewis, Oct 17 2008

Links

Table of n, a(n) for n=1..81.

Polish Math Olympiad 2008 Round 1 Question 1 on Art of Problem Solving Forum [From Joel B. Lewis, Oct 17 2008]

Formula

a(n, k) = n*k if min(n, k) = 1, n+k otherwise.

Example

Table begins
  1,  2,  3,  4,  5,  6,  7, ...
  2,  4,  5,  6,  7,  8,  9, ...
  3,  5,  6,  7,  8,  9, 10, ...
  4,  6,  7,  8,  9, 10, 11, ...
  5,  7,  8,  9, 10, 11, 12, ...
  ...

Crossrefs

Cf. A063711.

Initial row is A001477.

Sequence in context: A064514 A112342 A256094 * A340458 A185977 A204006

Adjacent sequences: A063709 A063710 A063711 * A063713 A063714 A063715

Keyword

nonn,easy,tabl

Author

Frank Seaton Taylor (ftaylor(AT)cse.ogi.edu), Aug 09 2001

Status

approved