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

0,2

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.

Links

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

Formula

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

Example

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.

Prog

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

Crossrefs

Cf. A091298, A208447.

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

Sequence in context: A350726 A241795 A289399 * A076207 A134057 A128281

Adjacent sequences: A306090 A306091 A306092 * A306094 A306095 A306096

Keyword

nonn

Author

M. F. Hasler, Sep 22 2018

Extensions

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

Status

approved