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Search: id:A080577
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| A080577 |
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Triangle in which n-th row lists all partitions of n in the order produced by Mathematica. |
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+0
23
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| 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 4, 3, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 5, 4, 1, 3, 2, 3, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 6, 5, 1, 4, 2, 4, 1, 1, 3, 3, 3, 2, 1, 3, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 6, 1, 5, 2, 5, 1, 1, 4, 3, 4, 2, 1, 4, 1, 1, 1, 3, 3, 1, 3, 2
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This is the "Mathematica" ordering of the partitions, referenced in numerous other sequences. The partitions of each integer are in reverse order of the conjugates of the partitions in Abramowitz and Stegun order (A036036). They are in the reverse of the order of the partitions in Maple order (A080576). - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Oct 18 2006
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LINKS
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Franklin T. Adams-Watters, First 20 rows, flattened
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
A. M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions
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EXAMPLE
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First five rows are:
{{1}}
{{2}, {1, 1}}
{{3}, {2, 1}, {1, 1, 1}}
{{4}, {3, 1}, {2, 2}, {2, 1, 1}, {1, 1, 1, 1}}
{{5}, {4, 1}, {3, 2}, {3, 1, 1}, {2, 2, 1}, {2, 1, 1, 1}, {1, 1, 1, 1, 1}}
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MATHEMATICA
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<<DiscreteMath`Combinatorica`; Partition[6]
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CROSSREFS
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See A080576 for the Maple version.
Differs from A036037 at a(48).
Cf. A036036.
Sequence in context: A026792 A139100 A036037 this_sequence A030312 A030321 A030305
Adjacent sequences: A080574 A080575 A080576 this_sequence A080578 A080579 A080580
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KEYWORD
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nonn,tabf
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mar 23 2003
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