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

Author

M. F. Hasler, Oct 16 2018

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A091298, A208447.

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

Programs

PARI

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

Formula

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