A209593 T(n,k)=Number of n X n 0..k arrays with every element equal to a diagonal or antidiagonal reflection.

2, 3, 16, 4, 81, 192, 5, 256, 3645, 9216, 6, 625, 28672, 1476225, 663552, 7, 1296, 140625, 51380224, 996451875, 191102976, 8, 2401, 513216, 791015625, 161128382464, 6053445140625, 82556485632, 9, 4096, 1529437, 7316407296

Offset: 1

Author

R. H. Hardin Mar 10 2012

Keywords

• nonn
• tabl

Comments

Table starts

......2.........3............4.............5...............6................7

.....16........81..........256...........625............1296.............2401

....192......3645........28672........140625..........513216..........1529437

...9216...1476225.....51380224.....791015625......7316407296......47738317081

.663552.996451875.161128382464.8009033203125.191221621088256.2767247026234327

Examples

			Some solutions for n=3 k=3
..2..0..1....1..0..1....0..0..3....0..2..1....1..2..3....0..1..2....2..2..0
..3..1..0....0..1..0....2..1..0....2..3..2....2..3..0....1..3..2....1..0..2
..0..3..3....1..0..1....1..2..3....3..2..3....2..0..2....2..2..2....1..1..3
		

Links

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

Crossrefs

Row 2 is A000583(n+1)

Formula

T(n,k) = (k+1) ^ (2n-(n modulo 2)) * ((k+1)*(2k+1)) ^ ((n*n-2n+(n modulo 2))/4)