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Search: id:A098529
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| A098529 |
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Triangle read by rows: T(n,k) counts plane partitions of n+1 that can be 'shrunk' in k ways to a plane partition of n by removing 1 element from it. Equivalently, it counts how many partitions of n+1 have k different partitions of n it just covers. |
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3
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| 1, 3, 3, 3, 6, 6, 1, 3, 18, 3, 9, 24, 15, 3, 42, 38, 3, 10, 60, 69, 21, 6, 72, 153, 45, 6, 9, 114, 220, 141, 15, 1, 3, 120, 399, 274, 60, 3, 18, 159, 558, 570, 162, 12, 3, 174, 834, 1029, 399, 46, 9, 267, 1080, 1749, 921, 138, 3
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Sequence starts 1; 3; 3,3; 6,6,1; 3,18,3; 9,24,15; 3,42,38,3; Row sums are A000219= the plane partitions of n+1 apart from offset. Sum(all k, k * T(n,k) ) = A090984(n) by definition. First column is A007425. Row lengths are A120565. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 14 2006
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EXAMPLE
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T(4,1)=2 because the only plane partitions of 4+1=5 that can be shrunk in only 1 way to plane partitions of 4 are {{5}} and {{1},{1},{1},{1},{1}}, producing {{4}} and {{1},{1},{1},{1}} respectively.
T(4,1)=3 because the only plane partitions of 4+1=5 that can be shrunk in only 1 way to plane partitions of 4 are {{5}},{{1,1,1,1,1}} and {{1},{1},{1},{1},{1}}, producing {{4}},{{1,1,1,1}} and {{1},{1},{1},{1}} respectively.
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MATHEMATICA
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(* functions 'planepartitions' and 'coversplaneQ', see A096574 *) Table[Frequencies[Count[planepartitions[n], q_/; coversplaneQ[ #, q]]&/@ planepartitions[n+1]], {n, 1, 12}]
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CROSSREFS
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Cf. A000219, A090984, A007425, A120565.
Sequence in context: A158315 A134059 A112669 this_sequence A133774 A108581 A073080
Adjacent sequences: A098526 A098527 A098528 this_sequence A098530 A098531 A098532
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KEYWORD
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more,nonn,tabf
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), Sep 12 2004
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EXTENSIONS
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Corrected and extended by Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 14 2006
More terms from Wouter Meeussen (wouter.meeussen(AT)pandora.be), May 05 2007
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