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Search: id:A059797
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| A059797 |
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Second in a series of arrays counting standard tableaux by partition type. |
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+0
9
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| 2, 5, 5, 9, 16, 9, 14, 35, 35, 14, 20, 64, 90, 64, 20, 27, 105, 189, 189, 105, 27, 35, 160, 350, 448, 350, 160, 35, 44, 231, 594, 924, 924, 594, 231, 44
(list; table; graph; listen)
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OFFSET
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0,1
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COMMENT
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The first array in the series is Pascal's triangle, A007318. The initial partition for each subsequent array in the series is chosen as described in A053445. When cells are squared, as in A008459,row sums yield 1 2 6 24 ...A000142. E.g.(1 + 16 + 36 + 16 + 1) + (25 + 25) = 70 + 50 = 120 using row five from A007318 and row two from this array.
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REFERENCES
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Stanton and White, Constructive Combinatorics, 1986, pp. 84, 91.
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FORMULA
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T(row, col) = T(row, col-1) + T(row-1, col) + A007318(row'+'col', col')
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EXAMPLE
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a(5) = 16 because we can write T(2,2) = T(1,2) + T(2,1) + A007318(3,3) = 5 + 5 + 6.
2; 5,5; 9,16,9; 14,35,35,14; ...
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CROSSREFS
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Cf. A000041, A000142, A007318, A008459, A053445.
Sequence in context: A126357 A070243 A050175 this_sequence A034387 A081240 A132295
Adjacent sequences: A059794 A059795 A059796 this_sequence A059798 A059799 A059800
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KEYWORD
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nice,nonn,tabl
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AUTHOR
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Alford Arnold (Alford1940(AT)aol.com), Feb 22 2001
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EXTENSIONS
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Recurrence corrected by Kevin Wilson (khwilson(AT)math.princeton.edu), Sep 14 2009
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