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%I #13 Jul 29 2020 03:46:01
%S 1,2,3,5,9,13,21,37,55,91,163,244,406,730,1054,1702,2998,4456,7372,
%T 13204,19765,32887,59131,85411,137971,243091,361351,597871,1070911,
%U 1603081,2667421,4796101,6927701,11190901,19717301,29309501,48493901,86862701,130027601
%N a(n) = 1 + Max_{0<=i<=j<=k; i+j+k=n-1} a(i)*a(j)*a(k) for n>0, with a(0) = 1.
%C a(n) is the maximum number of antichains (including the empty antichain) among all posets of size n with a Hasse diagram corresponding to a ternary tree (each node has up to three children). Equivalently, a(n)-1 is the maximum number of subtrees containing the root among all ternary trees of size n.
%C a(n)^(1/n) converges, and the decimal expansion of the limit seems to start with 1.6296636...
%F a(n) = 1 + Max_{0<=i<=j<=k; i+j+k=n-1} a(i)*a(j)*a(k) for n>0, a(0) = 1.
%e For n = 1 we have a(1) = 1 + a(0)*a(0)*a(0) = 1 + 1*1*1 = 2.
%e For n = 6 we have a(6) = 1 + a(1)*a(1)*a(3) = 1 + 2*2*5 = 21.
%e For n = 24 we have a(24) = 1 + a(4)*a(6)*a(13) = 1+9*21*730 = 137971.
%Y Ternary version of A091980.
%K easy,nonn
%O 0,2
%A _Justin Dallant_, Jul 28 2020
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