A115982 Number of planar partitions that are not corners.

0, 0, 0, 1, 3, 10, 23, 54, 112, 228, 437, 826, 1499, 2685, 4688, 8079, 13668, 22875, 37738, 61676, 99672, 159742, 253681, 399962, 625741, 972756, 1502302, 2306988, 3522492, 5351239, 8088469, 12170163, 18229411, 27192571

Offset

1,5

Comments

a(n) can also be approximated by considering A000094 since A000094(n) = A000041(n) - n = 0 0 0 1 2 5 8 14 21 32 ... with partial sums 0 0 0 1 3 8 16 30 51 83 ... which counts many of the initial cases. The remaining cases form 0 0 0 0 0 2 7 24 ... counting for n=6, 22/11 and 21/21.

Links

Table of n, a(n) for n=1..34.

Formula

a(n) = A000219(n) - A006330(n)

Example

The planar partitions begin 1 3 6 13 24 48 ... A000219 with corners 1 3 6 12 21 38 ... A006330; therefore the present sequence begins 0 0 0 1 3 10 ...

Crossrefs

Cf. A000219, A006330, A000041, A000094.

Sequence in context: A192973 A294503 A080204 * A167243 A316403 A185828

Adjacent sequences: A115979 A115980 A115981 * A115983 A115984 A115985

Keyword

easy,nonn

Author

Alford Arnold, Feb 17 2006

Extensions

Edited with additional terms by Franklin T. Adams-Watters, Mar 10 2006

Status

approved