A098529 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.

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

Offset

0,2

Comments

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. - Franklin T. Adams-Watters, Jun 14 2006

Links

Table of n, a(n) for n=0..56.

Example

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.

Mathematica

(* functions 'planepartitions' and 'coversplaneQ', see A096574 *) Table[Frequencies[Count[planepartitions[n], q_/; coversplaneQ[ #, q]]&/@ planepartitions[n+1]], {n, 1, 12}]

Crossrefs

Cf. A000219, A090984, A007425, A120565.

Sequence in context: A219686 A367761 A112669 * A133774 A108581 A073080

Adjacent sequences: A098526 A098527 A098528 * A098530 A098531 A098532

Keyword

more,nonn,tabf

Author

Wouter Meeussen, Sep 12 2004

Extensions

Corrected and extended by Franklin T. Adams-Watters, Jun 14 2006

More terms from Wouter Meeussen, May 05 2007

Status

approved