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A115722 Table of Durfee square of partitions in Mathematica order.

%I A115722 #11 Feb 16 2025 08:33:00
%S A115722 0,1,1,1,1,1,1,1,1,2,1,1,1,1,2,1,2,1,1,1,1,2,1,2,2,1,2,2,1,1,1,1,2,1,
%T A115722 2,2,1,2,2,2,1,2,2,1,1,1,1,2,1,2,2,1,2,2,2,2,1,2,2,2,2,1,2,2,2,1,1,1,
%U A115722 1,2,1,2,2,1,2,2,2,2,1,2,2,2,2,2,1,3,2,2,2,2,2,1,2,2,2,1,1,1,1,2,1,2,2,1,2
%N A115722 Table of Durfee square of partitions in Mathematica order.
%H A115722 Michael De Vlieger, <a href="/A115722/b115722.txt">Table of n, a(n) for n = 0..11731</a> (rows 0 <= n <= 26).
%H A115722 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DurfeeSquare.html">Durfee Square.</a>
%F A115722 If partition is laid out in descending order p(1),p(2),...,p(k) without repetition factors (e.g. [3,2,2,1,1,1]), a(P) = max_k min(k,p(k)).
%e A115722 First few rows:
%e A115722 0;
%e A115722 1,1;
%e A115722 1,1,1;
%e A115722 1,1,2,1,1;
%e A115722 1,1,2,1,2,1,1;
%t A115722 {0}~Join~Array[Map[Block[{k = Length@ #}, While[Nand[k > 0, AllTrue[Take[#, k], # >= k &]], k--]; k] &, IntegerPartitions@ #] &, 10] // Flatten (* _Michael De Vlieger_, Jan 17 2020 *)
%Y A115722 Cf. A115721, A115994, A115720, A080577.
%Y A115722 Row lengths A000041, totals A115995.
%K A115722 nonn,tabf
%O A115722 0,10
%A A115722 _Franklin T. Adams-Watters_, Mar 11 2006