A054645 Triangle T(n,k) of asymmetric n X n binary matrices with k=0..n^2 ones under action of dihedral group of the square D_4.

0, 0, 2, 6, 10, 10, 6, 2, 0, 0, 0, 1, 10, 63, 207, 525, 954, 1395, 1550, 1395, 954, 525, 207, 63, 10, 1, 0, 0, 1, 28, 258, 1503, 6475, 21810, 59540, 134333, 254178, 407040, 555356, 648054, 648054, 555356, 407040, 254178, 134333, 59540, 21810, 6475

Offset

3,3

Comments

Row sums give A054385.

Links

Table of n, a(n) for n=3..50.

Example

The batch [0,0,2,6,10,10,6,2,0,0] gives the numbers of asymmetric 3 X 3 binary matrices with k=0..9 ones under action of dihedral group of the square D_4.
There are 6 nonequivalent asymmetric 3 X 3 binary matrices with 3 ones under action of D_4:
[0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 1]
[0 0 1] [0 0 1] [0 1 0] [0 1 1] [1 0 1] [0 0 0]
[1 0 1] [1 1 0] [0 1 1] [1 0 0] [0 0 1] [1 1 0].

Crossrefs

Cf. A054252.

Sequence in context: A141257 A122882 A136700 * A337645 A225271 A357725

Adjacent sequences: A054642 A054643 A054644 * A054646 A054647 A054648

Keyword

nonn,tabf,nice

Author

Vladeta Jovovic, May 15 2000

Status

approved