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A115722 Table of Durfee square of partitions in Mathematica order. 7
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 (list; graph; refs; listen; history; text; internal format)
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
Row lengths A000041, totals A115995.
Sequence in context: A143223 A063993 A353445 * A115721 A279497 A359305
KEYWORD
nonn,tabf
AUTHOR
STATUS
approved

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Last modified February 21 03:52 EST 2024. Contains 370219 sequences. (Running on oeis4.)