A115722 Table of Durfee square of partitions in Mathematica order.

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, 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, 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

Offset: 0

Author

Franklin T. Adams-Watters, Mar 11 2006

Keywords

• nonn
• tabf

Examples

			First few rows:
0;
1,1;
1,1,1;
1,1,2,1,1;
1,1,2,1,2,1,1;
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..11731 (rows 0 <= n <= 26).
• Eric Weisstein's World of Mathematics, Durfee Square.

Crossrefs

Cf. A115721, A115994, A115720, A080577.

Row lengths A000041, totals A115995.

Programs

Mathematica

{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 *)

Formula

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)).