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

0,10

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.

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)).

Example

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

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 *)

Crossrefs

Cf. A115721, A115994, A115720, A080577.

Row lengths A000041, totals A115995.

Sequence in context: A143223 A063993 A353445 * A115721 A279497 A359305

Adjacent sequences: A115719 A115720 A115721 * A115723 A115724 A115725

Keyword

nonn,tabf

Author

Franklin T. Adams-Watters, Mar 11 2006

Status

approved