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

Author

M. F. Hasler, Sep 22 2018

Keywords

• nonn

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.

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A091298, A208447.

Column 4 of A306100 and A306101. See A306099 and A306093 for columns 2 and 3.

Programs

PARI

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

Formula

a(n) = Sum_{k=1..n} A091298(n,k)*4^k.

Extensions

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