

A306094


Number of plane partitions of n where parts are colored in (at most) 4 colors.


6



1, 4, 36, 228, 1540, 8964, 56292, 316388, 1857028, 10301892, 57884132, 312915172, 1720407492, 9132560068, 48898964964, 256790538660, 1350883911620, 6992031608260, 36296271612324, 185785685287076, 952221494828996, 4831039856692356, 24489621255994276
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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 four 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)*4^k.


EXAMPLE

For n = 1, there is only the partition [1], which can be colored in any of the four colors, whence a(1) = 4.
For n = 2, there are the partitions [2], [1,1] and [1;1]. Adding colors, this yields a(2) = 4 + 16 + 16 = 36 distinct possibilities.


PROG

(PARI) a(n)=!n+sum(k=1, n, A091298(n, k)*4^k)


CROSSREFS

Cf. A091298, A208447.
Column 4 of A306100 and A306101. See A306099 and A306093 for columns 2 and 3.
Sequence in context: A074434 A257888 A197424 * A018217 A003488 A295411
Adjacent sequences: A306091 A306092 A306093 * A306095 A306096 A306097


KEYWORD

nonn


AUTHOR

M. F. Hasler, Sep 22 2018


EXTENSIONS

a(12) corrected and a(13)a(22) added by Alois P. Heinz, Sep 24 2018


STATUS

approved



