A097994 - OEIS

A097994

T(n,k) counts plane partitions of n that can be 'extended' in (k+2) ways to a plane partition of n+1 by adding 1 element to it. Equivalently, it counts how many partitions of n have (k+2) different partitions of n+1 just covering it.

1, 3, 0, 3, 3, 0, 6, 6, 0, 1, 3, 15, 3, 3, 0, 9, 21, 6, 12, 0, 0, 3, 34, 21, 25, 3, 0, 0, 10, 45, 36, 54, 15, 0, 0, 0, 6, 54, 72, 108, 36, 6, 0, 0, 0, 9, 84, 102, 172, 117, 15, 0, 1, 0, 0, 3, 84, 174, 306, 228, 54, 7, 3, 0, 0, 0, 18, 114, 225, 483, 447, 162, 18, 12, 0, 0, 0, 0, 3, 114

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OFFSET

1,2

COMMENTS

The first column starts a t k=3 since all plane partitions can be extended in at least 3 ways. Row sums are A000219 by definition. Sum T(n,k) (k+2) =A090984.

LINKS

Table of n, a(n) for n=1..80.

EXAMPLE

T(4,4)=1 because {{2,1},{1}} is the only plane partition of 4 that can be extended in 4+2 = 6 ways to a plane partition of 5.

MATHEMATICA

(* functions 'planepartitions' and 'coversplaneQ', see A096574 *) Table[Frequencies[Count[planepartitions[n+1], q_/; coversplaneQ[q, # ]]&/@ planepartitions[n]], {n, 1, 16}]

CROSSREFS

Cf. A000219, A090984.

Sequence in context: A376229 A127801 A096597 * A318050 A053604 A375064

Adjacent sequences: A097991 A097992 A097993 * A097995 A097996 A097997

KEYWORD

hard,nonn,tabl

AUTHOR

Wouter Meeussen, Sep 07 2004

STATUS

approved