A306096 Number of plane partitions of n where parts are colored in (at most) 6 colors.

1, 6, 78, 726, 7278, 62574, 586878, 4889166, 42892710, 354335982, 2976581670, 23990771094, 197564663094, 1565310230790, 12548473437822, 98526949264374, 776195574339102, 6008457242324814, 46729763436714126, 357901583160822990, 2748384845416097718

Offset

0,2

Comments

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

Links

M. F. Hasler, Table of n, a(n) for n = 0..50

Formula

a(n) = Sum_{k=1..n} A091298(n,k)*6^k, for n > 0.

Example

For n = 1, there is only the partition [1], which can be colored in any of the six colors, whence a(1) = 6.
For n = 2, there are the partitions [2], [1,1] and [1;1]. Adding colors, this yields a(2) = 6 + 36 + 36 = 78 distinct possibilities.

Prog

(PARI) a(n)=sum(k=1, n, A091298(n, k)*6^k, !n)

Crossrefs

Cf. A091298, A208447.

Column 6 of A306100 and A306101. See A306099, A306093, A306094, A306095 for columns 2, 3, 4 and 5.

Sequence in context: A160240 A069669 A145359 * A370714 A145360 A183405

Adjacent sequences: A306093 A306094 A306095 * A306097 A306098 A306099

Keyword

nonn

Author

M. F. Hasler, Oct 16 2018

Status

approved