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%I A306093 #17 Oct 16 2018 23:09:22
%S A306093 1,3,21,102,525,2334,11100,47496,210756,886080,3759114,15378051,
%T A306093 63685767,255417357,1030081827,4078689249,16150234665,62991117084,
%U A306093 245948154087,947944122906,3653360869998,13946363438502,53149517598207,200994216333375,759191650345380
%N A306093 Number of plane partitions of n where parts are colored in 3 colors.
%C A306093 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.
%H A306093 Alois P. Heinz, <a href="/A306093/b306093.txt">Table of n, a(n) for n = 0..50</a>
%F A306093 a(n) = Sum_{k=1..n} A091298(n,k)*3^k.
%e A306093 For n = 1, there is only the partition [1], which can be colored in any of the three colors, whence a(1) = 3.
%e A306093 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.
%o A306093 (PARI) a(n)=sum(k=1,n,A091298(n,k)*3^k,!n)
%Y A306093 Cf. A091298, A208447.
%Y A306093 Column 3 of A306100 and A306101. See A306099 for column 2, A306094 .. A306096 for columns 4 .. 6.
%K A306093 nonn
%O A306093 0,2
%A A306093 _M. F. Hasler_, Sep 22 2018
%E A306093 a(12) corrected and a(13)-a(24) added by _Alois P. Heinz_, Sep 24 2018

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