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A105805
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Dyson's rank of partitions listed in the Abramowitz-Stegun order.
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7
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0, 1, -1, 2, 0, -2, 3, 1, 0, -1, -3, 4, 2, 1, 0, -1, -2, -4, 5, 3, 2, 1, 1, 0, -1, -1, -2, -3, -5, 6, 4, 3, 2, 2, 1, 0, 0, 0, -1, -2, -2, -3, -4, -6, 7, 5, 4, 3, 2, 3, 2, 1, 1, 0, 1, 0, -1, -1, -2, -1, -2, -3, -3, -4, -5, -7, 8, 6, 5, 4, 3, 4, 3, 2, 1, 2, 1, 0, 2, 1, 0, 0, -1, -1, 0, -1, -2, -2, -3, -2, -3, -4, -4, -5, -6, -8, 9, 7, 6, 5, 4, 3, 5, 4, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| The sequence of row lengths of this array is [1,2,3,5,7,11,15,22,30,42,56,77,...] from A000041(n), n>=1 (partition numbers).
Just for n <= 6, row n is antisymmetric due to conjugation of partitions (see links under A105806): a(n,p(n)-(k-1)) = a(n,k), k = 1,...,floor(p(n)/2). [Comment corrected by Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 17 2006]
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REFERENCES
| F. J. Dyson: Problems for solution nr. 4261, Am. Math. Month. 54 (1947) 418.
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LINKS
| 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, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, pp. 831-2.
W. Lang: First 15 rows.
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FORMULA
| a(n, k)= rank of the k-th partition of n in Abramowitz-Stegun order (see reference). The rank of a partition is the maximal part minus the number of parts (m in the table of Abramowitz-Stegun).
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EXAMPLE
| [0]; [1,-1]; [2,0,-2]; [3,1,0,-1,-3]; [4,2,1,0,-1,-2,-4]; [5,3,2,1,1,0,-1,-1,-2,-3,-5]; ...
Row 3 for partitions of 3 in the mentioned order: 3,(1,2),1^3 with ranks 2,0,-2.
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CROSSREFS
| Sequence in context: A087509 A181871 A089596 * A194547 A049581 A114327
Adjacent sequences: A105802 A105803 A105804 * A105806 A105807 A105808
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KEYWORD
| sign,easy,tabf
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Apr 28 2005
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