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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 (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 four given colors, since there is no term at all.
LINKS
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
Column 4 of A306100 and A306101. See A306099 and A306093 for columns 2 and 3.
Sequence in context: A074434 A257888 A197424 * A018217 A003488 A295411
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

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Last modified June 24 00:02 EDT 2024. Contains 373661 sequences. (Running on oeis4.)