A275798
One half of the number of n X n square grids with squares of two colors modulo operations of the dihedral group D_4.
Original entry on oeis.org
1, 3, 51, 4274, 2105872, 4295278656, 35184441295872, 1152921514002096128, 151115727460762179076096, 79228162514269052299408048128, 166153499473114502703835144588886016, 1393796574908163946384646767619026404245504, 46768052394588893382518536034792338549485151977472
Offset: 1
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.
Original entry on oeis.org
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
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].
A109721
Number of different ways of selecting n nonempty cells in a 4 X 4 binary matrix, excluding all rotationally and symmetrically equivalent matrices.
Original entry on oeis.org
1, 3, 21, 77, 252, 567, 1051, 1465, 1674, 1465, 1051, 567, 252, 77, 21, 3, 1
Offset: 0
Original entry on oeis.org
1, 3, 19, 271, 7085, 251429, 10997806, 564316854, 33175912910, 2196968168590, 161790768056642, 13114202824936638, 1160158996141467678, 111226473580172327222, 11486922450679555836573
Offset: 1
a(6) = 1 + 2 + 16 + 252 + 6814 + 244344 = 251429 is prime.
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