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A215294 Number of permutations of 0..floor((n*3-2)/2) on odd squares of an n X 3 array such that each row and column of odd squares is increasing. 1
1, 3, 6, 30, 70, 420, 1050, 6930, 18018, 126126, 336336, 2450448, 6651216, 49884120, 137181330, 1051723530, 2921454250, 22787343150, 63804560820, 504636071940, 1422156202740, 11377249621920, 32235540595440, 260363981732400 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 3 of A215297.

a(n) is number of symmetric standard Young tableaux of shape (n,n,n). - Ran Pan, May 21 2015

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

Ran Pan, Problem 4, Project P.

FORMULA

f3 = floor((n+1)/2), f4 = floor(n/2);

a(n) = A060854(1,f3)*A060854(2,f4)*binomial(1*f3+2*f4,1*f3).

EXAMPLE

Some solutions for n=5

..x..1..x....x..0..x....x..0..x....x..4..x....x..0..x....x..1..x....x..1..x

..0..x..5....2..x..4....2..x..5....0..x..2....1..x..2....0..x..5....0..x..3

..x..3..x....x..1..x....x..1..x....x..5..x....x..3..x....x..2..x....x..2..x

..2..x..6....3..x..6....3..x..6....1..x..3....4..x..6....3..x..6....4..x..5

..x..4..x....x..5..x....x..4..x....x..6..x....x..5..x....x..4..x....x..6..x

CROSSREFS

Sequence in context: A136946 A125521 A211168 * A090932 A280981 A265376

Adjacent sequences:  A215291 A215292 A215293 * A215295 A215296 A215297

KEYWORD

nonn

AUTHOR

R. H. Hardin, Aug 07 2012

STATUS

approved

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Last modified September 26 06:54 EDT 2017. Contains 292502 sequences.