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%I #3 Mar 31 2012 13:21:32
%S 0,1,1,2,3,3,3,4,4,5,6,6,6,6,7,7,7,8,8,9,10,10,10,10,10,11,11,11,11,
%T 12,12,12,13,13,14,15,15,15,15,15,15,16,16,16,16,16,17,17,17,17,18,18,
%U 18,19,19,20,21,21,21,21,21,21,21,22,22,22,22,22,22,23,23,23,23,23,24,24
%N Maximum over all planar partitions of n of the number of ways the partition can be shrunk by removing a single element.
%C Maximum of any sum_i k_i, where sum_i k_i*(k_i+1)/2 <= n.
%F For n > 2, let m be the largest value such that tetrahedral number m*(m+1)*(m+2)/6 <= n. Then a(n) = max(m*(m+1)/2, m+1 + a(n - (m+1)*(m+2)/2)), taking a(k) to be 0 for k < 0.
%Y Row lengths of A098529.
%K nonn
%O 0,4
%A _Franklin T. Adams-Watters_, Jun 14 2006
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