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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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.

Original entry on oeis.org

1, 4, 32, 400, 6660, 138576, 3460464, 100821904, 3357239440
Offset: 0

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Author

Ludovic Schwob, May 20 2024

Keywords

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.

Examples

			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

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