A306094 Number of plane partitions of n where parts are colored in (at most) 4 colors.

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

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