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 A063712 Table of bits required for product of n- and k-bit positive numbers read by antidiagonals. 1

%I

%S 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,

%T 9,8,9,10,10,10,10,10,10,10,9,10,11,11,11,11,11,11,11,11,10,11,12,12,

%U 12,12,12,12,12,12,12,11,12,13,13,13,13,13,13,13,13,13,13,12,13,14,14

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

%C This sequence is A063711 without zeros.

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

%C 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

%H Polish Math Olympiad 2008 Round 1 Question 1 on <a href="http://www.artofproblemsolving.com/Forum/viewtopic.php?t=232205">Art of Problem Solving Forum</a> [From _Joel B. Lewis_, Oct 17 2008]

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

%e Table begins

%e 1, 2, 3, 4, 5, 6, 7, ...

%e 2, 4, 5, 6, 7, 8, 9, ...

%e 3, 5, 6, 7, 8, 9, 10, ...

%e 4, 6, 7, 8, 9, 10, 11, ...

%e 5, 7, 8, 9, 10, 11, 12, ...

%e ...

%Y Cf. A063711.

%Y Initial row is A001477.

%K nonn,easy,tabl

%O 1,2

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

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Last modified June 18 01:16 EDT 2021. Contains 345098 sequences. (Running on oeis4.)