

A306093


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


7



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
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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



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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



