%I #10 Oct 16 2018 23:05:25
%S 1,4,36,228,1540,8964,56292,316388,1857028,10301892,57884132,
%T 312915172,1720407492,9132560068,48898964964,256790538660,
%U 1350883911620,6992031608260,36296271612324,185785685287076,952221494828996,4831039856692356,24489621255994276
%N Number of plane partitions of n where parts are colored in (at most) 4 colors.
%C 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.
%H Alois P. Heinz, <a href="/A306094/b306094.txt">Table of n, a(n) for n = 0..50</a>
%F a(n) = Sum_{k=1..n} A091298(n,k)*4^k.
%e For n = 1, there is only the partition [1], which can be colored in any of the four colors, whence a(1) = 4.
%e 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.
%o (PARI) a(n)=!n+sum(k=1,n,A091298(n,k)*4^k)
%Y Cf. A091298, A208447.
%Y Column 4 of A306100 and A306101. See A306099 and A306093 for columns 2 and 3.
%K nonn
%O 0,2
%A _M. F. Hasler_, Sep 22 2018
%E a(12) corrected and a(13)-a(22) added by _Alois P. Heinz_, Sep 24 2018