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 A306093 Number of plane partitions of n where parts are colored in 3 colors. 7
 1, 3, 21, 102, 525, 2334, 11100, 47496, 210756, 886080, 3759114, 15378051, 63685767, 255417357, 1030081827, 4078689249, 16150234665, 62991117084, 245948154087, 947944122906, 3653360869998, 13946363438502, 53149517598207, 200994216333375, 759191650345380 (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 three 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)*3^k. EXAMPLE For n = 1, there is only the partition [1], which can be colored in any of the three colors, whence a(1) = 3. For n = 2, there are the partitions [2], [1,1] and [1;1]. Adding colors, this yields a(2) = 3 + 9 + 9 = 21 distinct possibilities. PROG (PARI) a(n)=sum(k=1, n, A091298(n, k)*3^k, !n) CROSSREFS Cf. A091298, A208447. Column 3 of A306100 and A306101. See A306099 for column 2, A306094 .. A306096 for columns 4 .. 6. Sequence in context: A350726 A241795 A289399 * A076207 A134057 A128281 Adjacent sequences: A306090 A306091 A306092 * A306094 A306095 A306096 KEYWORD nonn AUTHOR M. F. Hasler, Sep 22 2018 EXTENSIONS a(12) corrected and a(13)-a(24) added by Alois P. Heinz, Sep 24 2018 STATUS approved

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Last modified June 19 16:49 EDT 2024. Contains 373503 sequences. (Running on oeis4.)