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A373027
Number of (0,1)-matrices with sum of entries equal to 2*n or 2*n+1, no zero rows or columns, which are centrally symmetric.
1
1, 4, 32, 400, 6660, 138576, 3460464, 100821904, 3357239440
OFFSET
0,2
COMMENTS
a(n) is the number ordered pairs of semistandard Young tableaux of size 2*n or 2*n+1 with consecutive entries (i.e., if i is in T, and 1<=j<=i, then j is in T) and with conjugate shapes, which are both invariant under Schützenberger involution.
EXAMPLE
The a(2) = 32 matrices with sum of entries equal to 4:
[1 0 0 0] [0 0 0 1] [1 0 0 0] [0 0 0 1] [0 0 1 0] [0 1 0 0]
[0 1 0 0] [0 1 0 0] [0 0 1 0] [0 0 1 0] [0 0 0 1] [1 0 0 0]
[0 0 1 0] [0 0 1 0] [0 1 0 0] [0 1 0 0] [1 0 0 0] [0 0 0 1]
[0 0 0 1] [1 0 0 0] [0 0 0 1] [1 0 0 0] [0 1 0 0] [0 0 1 0]
.
[0 1 0 0] [0 0 1 0] [1 0 0] [0 1 0] [0 1 0] [0 0 1]
[0 0 0 1] [1 0 0 0] [0 1 0] [1 0 0] [0 0 1] [0 1 0]
[1 0 0 0] [0 0 0 1] [0 1 0] [0 0 1] [1 0 0] [0 1 0]
[0 0 1 0] [0 1 0 0] [0 0 1] [0 1 0] [0 1 0] [1 0 0]
.
[1 0] [0 1] [1 0] [0 1] [1]
[1 0] [0 1] [0 1] [1 0] [1]
[0 1] [1 0] [1 0] [0 1] [1]
[0 1] [1 0] [0 1] [1 0] [1]
.
[1 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1] [0 1 0] [1 0] [0 1]
[0 1 1 0] [1 0 0 1] [1 0 0 1] [0 1 1 0] [1 0 1] [1 1] [1 1]
[0 0 0 1] [0 0 1 0] [0 1 0 0] [1 0 0 0] [0 1 0] [0 1] [1 0]
.
[1 1 0 0] [0 0 1 1] [1 0 1 0] [0 1 0 1] [1 1 0] [0 1 1] [1 1]
[0 0 1 1] [1 1 0 0] [0 1 0 1] [1 0 1 0] [0 1 1] [1 1 0] [1 1]
.
[1 1 1 1]
CROSSREFS
Sequence in context: A349558 A005263 A325574 * A113131 A367376 A195762
KEYWORD
nonn,more
AUTHOR
Ludovic Schwob, May 20 2024
STATUS
approved