

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
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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 2way 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(r1,c), A(r,c+1) and A(r,c1) 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 4834=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



