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Search: id:A100568
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| A100568 |
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Number of compositions of n(n^2+1)/2 into n distinct parts each no more than n^2. |
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+0
2
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| 1, 1, 4, 48, 2064, 167280, 23136480, 4824953280, 1417422988800, 557894688341760, 283527366696806400, 180770613278509900800, 141310830114906688051200, 132919668653581764822067200, 148111929489204170921816985600
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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In an n X n magic square, each row and column is a composition of type described.
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LINKS
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Henry Bottomley, Partition and composition calculator
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FORMULA
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a(n)=A000142(n)*A052456(n). a(n) is close to n^(2n-5/2)*sqrt(6/(pi*e)) in the sense that the ratio between the two tends to 1 as n increases. Experimentally, something like n^(2n) * sqrt(6 / (pi * e * (n^5 - 1.366...n^4 + 1.146...n^3 - 0.826...n^2 + 0.413...n + 0.115...))) seems to be even closer.
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EXAMPLE
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a(2)=4 since 5 can be written 1+4, 2+3, 3+2 or 4+1.
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CROSSREFS
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Adjacent sequences: A100565 A100566 A100567 this_sequence A100569 A100570 A100571
Sequence in context: A013145 A013150 A011266 this_sequence A112693 A136384 A123373
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Nov 28 2004
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