

A263412


Triangle read by rows: T(n>=0, 0<=k<=A161680(n)) is the number of standard tableaux of size n whose shape contains k attacking pairs.


2



1, 1, 1, 1, 1, 2, 0, 1, 1, 3, 0, 5, 0, 0, 1, 1, 4, 0, 11, 0, 5, 4, 0, 0, 0, 1, 1, 5, 0, 19, 0, 21, 10, 0, 9, 5, 5, 0, 0, 0, 0, 1, 1, 6, 0, 29, 0, 49, 20, 21, 35, 21, 15, 0, 28, 0, 0, 6, 0, 0, 0, 0, 0, 1, 1, 7, 0, 41, 0, 92, 35, 84, 90, 56, 91, 42, 134, 0, 0, 21, 28, 20, 14, 0, 0, 7, 0, 0, 0, 0, 0, 0, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,6


COMMENTS

Row sums give A000085.


LINKS

Alois P. Heinz, Rows n = 0..50, flattened
FindStat  Combinatorial Statistic Finder, The number of attacking pairs of a standard tableau.


EXAMPLE

Triangle begins:
1;
1;
1,1;
1,2,0,1;
1,3,0,5,0,0,1;
1,4,0,11,0,5,4,0,0,0,1;
1,5,0,19,0,21,10,0,9,5,5,0,0,0,0,1;
1,6,0,29,0,49,20,21,35,21,15,0,28,0,0,6,0,0,0,0,0,1;
1,7,0,41,0,92,35,84,90,56,91,42,134,0,0,21,28,20,14,0,0,7,0,0,0,0,0,0,1;
...


CROSSREFS

Cf. A000085, A161680.
Sequence in context: A055186 A217760 A339218 * A321258 A331510 A319854
Adjacent sequences: A263409 A263410 A263411 * A263413 A263414 A263415


KEYWORD

nonn,tabf


AUTHOR

Christian Stump, Oct 17 2015


EXTENSIONS

Two terms (for rows 0 and 1) prepended by Alois P. Heinz, Nov 15 2015


STATUS

approved



