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A306096 Number of plane partitions of n where parts are colored in (at most) 6 colors. 4
1, 6, 78, 726, 7278, 62574, 586878, 4889166, 42892710, 354335982, 2976581670, 23990771094, 197564663094, 1565310230790, 12548473437822, 98526949264374, 776195574339102, 6008457242324814, 46729763436714126, 357901583160822990, 2748384845416097718 (list; graph; refs; listen; history; text; internal format)
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
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
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
KEYWORD
nonn
AUTHOR
M. F. Hasler, Oct 16 2018
STATUS
approved

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Last modified July 17 15:56 EDT 2024. Contains 374377 sequences. (Running on oeis4.)