A306093 Number of plane partitions of n where parts are colored in 3 colors.

1, 3, 21, 102, 525, 2334, 11100, 47496, 210756, 886080, 3759114, 15378051, 63685767, 255417357, 1030081827, 4078689249, 16150234665, 62991117084, 245948154087, 947944122906, 3653360869998, 13946363438502, 53149517598207, 200994216333375, 759191650345380

Offset: 0

Author

M. F. Hasler, Sep 22 2018

Keywords

• nonn

Comments

a(0) = 1 corresponds to the empty sum, in which all terms are colored in one among three 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 three colors, whence a(1) = 3.
For n = 2, there are the partitions [2], [1,1] and [1;1]. Adding colors, this yields a(2) = 3 + 9 + 9 = 21 distinct possibilities.
		

Links

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

Crossrefs

Cf. A091298, A208447.

Column 3 of A306100 and A306101. See A306099 for column 2, A306094 .. A306096 for columns 4 .. 6.

Programs

PARI

a(n)=sum(k=1,n,A091298(n,k)*3^k,!n)

Formula

a(n) = Sum_{k=1..n} A091298(n,k)*3^k.

Extensions

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