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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. 2
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; refs; listen; history; text; internal format)
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: A219217 A219686 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

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Last modified November 18 22:35 EST 2019. Contains 329305 sequences. (Running on oeis4.)