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A306099 Number of plane partitions of n where parts are colored in 2 colors.

%I A306099 #18 Oct 16 2018 23:08:22
%S A306099 1,2,10,34,122,378,1242,3690,11266,32666,94994,267202,754546,2072578,
%T A306099 5691514,15364290,41321962,109634586,290048746,758630698,1977954706,
%U A306099 5111900410,13161995010,33645284962,85727394018,217042978882,547750831210,1375147078146,3441516792442
%N A306099 Number of plane partitions of n where parts are colored in 2 colors.
%C A306099 a(0) = 1 corresponds to the empty sum, in which all terms are colored in one among two given colors, since there is no term at all.
%H A306099 Alois P. Heinz, <a href="/A306099/b306099.txt">Table of n, a(n) for n = 0..50</a>
%H A306099 OEIS wiki: <a href="/wiki/Plane_partitions">Plane partitions</a>
%H A306099 Wikipedia, <a href="https://en.wikipedia.org/wiki/Plane_partition">Plane partition</a>
%F A306099 a(n) = Sum_{k=1..n} A091298(n,k)*2^k.
%e A306099 For n = 1, there is only the partition [1], which can be colored in any of the two colors, whence a(1) = 2.
%e A306099 For n = 2, there are the partitions [2], [1,1] and [1;1]. Adding colors, this yields a(2) = 2 + 4 + 4 = 10 distinct possibilities.
%o A306099 (PARI) a(n)=!n+sum(k=1,n,A091298(n,k)<<k)
%Y A306099 Cf. A091298, A208447.
%Y A306099 Column 2 of A306100 and A306101. See A306093 .. A306096 for columns 3 .. 6.
%K A306099 nonn
%O A306099 0,2
%A A306099 _M. F. Hasler_ and _Rick L. Shepherd_, following an idea from _David S. Newman_, Sep 22 2018
%E A306099 a(12) corrected and a(13)-a(28) added by _Alois P. Heinz_, Sep 24 2018