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A194446
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Number of parts in the n-th region of the set of partitions of j, if 1<=n<=A000041(j).
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30
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1, 2, 3, 1, 5, 1, 7, 1, 2, 1, 11, 1, 2, 1, 15, 1, 2, 1, 4, 1, 1, 22, 1, 2, 1, 4, 1, 2, 1, 30, 1, 2, 1, 4, 1, 1, 7, 1, 2, 1, 1, 42, 1, 2, 1, 4, 1, 2, 1, 8, 1, 1, 3, 1, 1, 56, 1, 2, 1, 4, 1, 1, 7, 1, 2, 1, 1, 12, 1, 2, 1, 4, 1, 2, 1, 1, 77, 1, 2, 1
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OFFSET
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1,2
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COMMENTS
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For the definition of "region" of the set of partitions of j, see A206437.
a(n) is also the number of positive integers in the n-th row of triangle A186114. a(n) is also the number of positive integers in the n-th row of triangle A193870.
Also triangle read by rows: T(j,k) = number of parts in the k-th region of the outer shell of the partitions of j. See example. For more information see A135010.
a(n) is also the length of the n-th vertical segment in the shell model of partitions. The length of the n-th horizontal segment is A141285(n). See also A194447. - Omar E. Pol, Mar 04 2012
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LINKS
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Table of n, a(n) for n=1..80.
O. E. Pol, Illustration of the seven regions of 5
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FORMULA
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a(n) = A141285(n) - A194447(n). - Omar E. Pol, Mar 04 2012
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EXAMPLE
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Written as an irregular triangle the sequence begins:
1;
2;
3;
1,5;
1,7;
1,2,1,11;
1,2,1,15;
1,2,1,4,1,1,22;
1,2,1,4,1,2,1,30;
1,2,1,4,1,1,7,1,2,1,1,42;
1,2,1,4,1,2,1,8,1,1,3,1,1,56;
1,2,1,4,1,1,7,1,2,1,1,12,1,2,1,4,1,2,1,1,77;
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CROSSREFS
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Row j has length A187219(j). Right border gives A000041, j >= 1. Records give A000041, j >= 1. Row sums give A138137.
Cf. A002865, A006128, A135010, A138121, A186114, A186412, A193870, A194436, A194437, A194438, A194439, A194447.
Sequence in context: A080305 A220137 A053815 * A166333 A173239 A214055
Adjacent sequences: A194443 A194444 A194445 * A194447 A194448 A194449
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KEYWORD
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nonn,tabf
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AUTHOR
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Omar E. Pol, Nov 26 2011
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STATUS
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approved
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