This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A120565 #3 Mar 31 2012 13:21:32 %S A120565 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 A120565 12,12,12,13,13,14,15,15,15,15,15,15,16,16,16,16,16,17,17,17,17,18,18, %U A120565 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 A120565 Maximum over all planar partitions of n of the number of ways the partition can be shrunk by removing a single element. %C A120565 Maximum of any sum_i k_i, where sum_i k_i*(k_i+1)/2 <= n. %F A120565 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 A120565 Row lengths of A098529. %K A120565 nonn %O A120565 0,4 %A A120565 _Franklin T. Adams-Watters_, Jun 14 2006