The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A263412 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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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.
(history; published version)

#11 by Alois P. Heinz at Sun Nov 15 18:53:44 EST 2015

STATUS

editing

approved

#10 by Alois P. Heinz at Sun Nov 15 18:48:47 EST 2015

LINKS

Alois P. Heinz, <a href="/A263412/b263412.txt">Rows n = 0..50, flattened</a>

#9 by Alois P. Heinz at Sun Nov 15 18:21:42 EST 2015

NAME

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

CROSSREFS

Cf. A000085, A161680.

#8 by Alois P. Heinz at Sun Nov 15 18:19:18 EST 2015

NAME

Triangle read by rows: T(n>=2, 0, k>=0) is the number of standard tableaux of size n whose shape contains k attacking pairs.

#7 by Alois P. Heinz at Sun Nov 15 18:19:00 EST 2015

DATA

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

OFFSET

2,4

0,6

COMMENTS

Row sums give A000085, n >= 2.

EXAMPLE

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,;

EXTENSIONS

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

STATUS

approved

editing

#6 by Bruno Berselli at Sat Oct 17 12:57:23 EDT 2015

STATUS

reviewed

approved

#5 by Joerg Arndt at Sat Oct 17 12:11:19 EDT 2015

STATUS

proposed

reviewed

#4 by Christian Stump at Sat Oct 17 10:52:46 EDT 2015

STATUS

editing

proposed

#3 by Christian Stump at Sat Oct 17 10:52:40 EDT 2015

NAME

Triangle read by rows: T(n>=2, k>=0) is the number of standard tableaux of size n and whose shape contains k attacking pairs.

#2 by Christian Stump at Sat Oct 17 08:45:35 EDT 2015

NAME

allocated for Christian StumpTriangle read by rows: T(n>=2, k>=0) is the number of standard tableaux of size n and k attacking pairs.

DATA

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

OFFSET

2,4

COMMENTS

Row sums give A000085, n >= 2.

LINKS

FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000016">The number of attacking pairs of a standard tableau</a>.

EXAMPLE

Triangle begins:

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.

KEYWORD

allocated

nonn,tabf

AUTHOR

Christian Stump, Oct 17 2015

STATUS

approved

editing