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 A306099 Number of plane partitions of n where parts are colored in 2 colors. 7
 1, 2, 10, 34, 122, 378, 1242, 3690, 11266, 32666, 94994, 267202, 754546, 2072578, 5691514, 15364290, 41321962, 109634586, 290048746, 758630698, 1977954706, 5111900410, 13161995010, 33645284962, 85727394018, 217042978882, 547750831210, 1375147078146, 3441516792442 (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 two given colors, since there is no term at all. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..50 OEIS wiki: Plane partitions Wikipedia, Plane partition FORMULA a(n) = Sum_{k=1..n} A091298(n,k)*2^k. EXAMPLE For n = 1, there is only the partition [1], which can be colored in any of the two colors, whence a(1) = 2. 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. PROG (PARI) a(n)=!n+sum(k=1, n, A091298(n, k)<

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Last modified June 1 19:32 EDT 2020. Contains 334762 sequences. (Running on oeis4.)