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A064410
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Number of partitions of n with zero crank.
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3
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0, 0, 1, 1, 1, 1, 1, 2, 2, 4, 4, 7, 7, 11, 12, 17, 19, 27, 30, 41, 48, 62, 73, 95, 110, 140, 166, 206, 243, 302, 354, 435, 513, 622, 733, 887, 1039, 1249, 1467, 1750, 2049, 2438, 2847, 3371, 3934, 4634
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OFFSET
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1,8
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COMMENTS
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For a partition p, let l(p) = largest part of p, w(p) = number of 1's in p, m(p) = number of parts of p larger than w(p). The crank of p is given by l(p) if w(p) = 0, otherwise m(p)-w(p).
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LINKS
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Table of n, a(n) for n=1..46.
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FORMULA
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a(n) = A000041(n)-2*A001522(n). a(n) = A064391(n, 0).
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EXAMPLE
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a(10)=4 because there are 4 partitions of 10 with zero crank: 1+1+2+3+3, 1+1+4+4, 1+1+3+5 and 1+9.
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CROSSREFS
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Cf. A064391, A000041, A001522.
Sequence in context: A099770 A099383 A197122 * A062896 A025065 A131524
Adjacent sequences: A064407 A064408 A064409 * A064411 A064412 A064413
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KEYWORD
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nonn,changed
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AUTHOR
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Vladeta Jovovic, Sep 29 2001
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EXTENSIONS
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More terms from Reiner Martin (reinermartin(AT)hotmail.com), Dec 26 2001
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STATUS
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approved
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