A306099 Number of plane partitions of n where parts are colored in 2 colors.

1, 2, 10, 34, 122, 378, 1242, 3690, 11266, 32666, 94994, 267202, 754546, 2072578, 5691514, 15364290, 41321962, 109634586, 290048746, 758630698, 1977954706, 5111900410, 13161995010, 33645284962, 85727394018, 217042978882, 547750831210, 1375147078146, 3441516792442

Offset

0,2

Comments

a(0) = 1 corresponds to the empty sum, in which all terms are colored in one among two given colors, since there is no term at all.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..50

OEIS wiki: Plane partitions

Wikipedia, Plane partition

Formula

a(n) = Sum_{k=1..n} A091298(n,k)*2^k.

Example

For n = 1, there is only the partition [1], which can be colored in any of the two colors, whence a(1) = 2.
For n = 2, there are the partitions [2], [1,1] and [1;1]. Adding colors, this yields a(2) = 2 + 4 + 4 = 10 distinct possibilities.

Prog

(PARI) a(n)=!n+sum(k=1, n, A091298(n, k)<<k)

Crossrefs

Cf. A091298, A208447.

Column 2 of A306100 and A306101. See A306093 .. A306096 for columns 3 .. 6.

Sequence in context: A351550 A119193 A124634 * A192378 A052965 A108924

Adjacent sequences: A306096 A306097 A306098 * A306100 A306101 A306102

Keyword

nonn

Author

M. F. Hasler and Rick L. Shepherd, following an idea from David S. Newman, Sep 22 2018

Extensions

a(12) corrected and a(13)-a(28) added by Alois P. Heinz, Sep 24 2018

Status

approved