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A063712
Table of bits required for product of n- and k-bit positive numbers read by antidiagonals.
1
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
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
KEYWORD
nonn,easy,tabl
AUTHOR
Frank Seaton Taylor (ftaylor(AT)cse.ogi.edu), Aug 09 2001
STATUS
approved