A252479 The number of planar partitions of n with adjacent parts differing by no more than 1.

1, 1, 3, 6, 11, 19, 34, 53, 89, 141, 224, 346, 542, 815, 1246, 1862, 2772, 4085, 6003, 8720, 12653, 18190, 26072, 37122, 52679, 74298, 104458, 146129, 203713, 282779, 391266

Offset

0,3

Comments

A000219 counts planar partitions of n, which are represented by arrays of positive integers A(r,c) that sum to n and are 2-way monotonic in the sense of A(r,c+1) <= A(r,c) and A(r+1,c) <= A(r,c). The sequence here imposes the additional constraint that the absolute difference between A(r,c) and any of the (up to 4) adjacent terms A(r+1,c), A(r-1,c), A(r,c+1) and A(r,c-1) is <=1.

Links

Table of n, a(n) for n=0..30.

Example

a(6)=34 and A000219(6) = 48 differ by 14 because the following 48-34=14 plane partitions of 6 are not counted here:
3 1 1 1 (and its transpose)
.
4 1 1 (and its transpose)
.
3 1
1
1     (and its transpose)
.
3 1
1 1
.
3 1
2     (and its transpose)
.
4 2 (and its transpose
.
4 1
1
.
5 1 (and its transpose)

Crossrefs

Cf. A000219, A034296.

Sequence in context: A281573 A262987 A191696 * A320850 A180086 A116365

Adjacent sequences: A252476 A252477 A252478 * A252480 A252481 A252482

Keyword

nonn,more

Author

R. J. Mathar, Jan 09 2015

Status

approved