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A252479 The number of planar partitions of n with adjacent parts differing by no more than 1. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 7 05:49 EDT 2022. Contains 357270 sequences. (Running on oeis4.)