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

Author

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

Keywords

• nonn

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.

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..50
• OEIS wiki: Plane partitions
• Wikipedia, Plane partition

Crossrefs

Cf. A091298, A208447.

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

Programs

PARI

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

Formula

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

Extensions

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