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Search: id:A063712
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| A063712 |
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Table of bits required for product of n- and k-bit positive numbers read by antidiagonals. |
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+0
2
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| 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
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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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 by 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.) [From Joel B. Lewis (jblewis(AT)post.harvard.edu), Oct 17 2008]
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LINKS
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Polish Math Olympiad 2008 Round 1 Question 1 on Art of Problem Solving Forum [From Joel B. Lewis (jblewis(AT)post.harvard.edu), Oct 17 2008]
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FORMULA
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a(n, k) = n*k if min(n, k) = 1, n+k otherwise.
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EXAMPLE
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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 ...
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CROSSREFS
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Cf. A063711.
Initial row is A001477.
Sequence in context: A061282 A064514 A112342 this_sequence A106251 A134478 A051162
Adjacent sequences: A063709 A063710 A063711 this_sequence A063713 A063714 A063715
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Frank Seaton Taylor (ftaylor(AT)cse.ogi.edu), Thu, Aug 09 2001
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