A204106 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) such that b(i,j)*b(i-1,j)-c(i,j)*c(i,j-1) is nonzero.

36, 144, 144, 576, 864, 576, 2304, 5184, 5184, 2304, 9216, 31104, 46656, 31104, 9216, 36864, 186624, 419904, 419904, 186624, 36864, 147456, 1119744, 3779136, 5738688, 3779136, 1119744, 147456, 589824, 6718464, 34012224, 78428736, 78428736

Offset: 1

Author

R. H. Hardin Jan 10 2012

Keywords

• nonn
• tabl

Comments

Also 0..2 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements

Table starts

.....36......144........576.........2304...........9216............36864

....144......864.......5184........31104.........186624..........1119744

....576.....5184......46656.......419904........3779136.........34012224

...2304....31104.....419904......5738688.......78428736.......1073134656

...9216...186624....3779136.....78428736.....1631513664......34026967296

..36864..1119744...34012224...1073134656....34026967296....1084257353088

.147456..6718464..306110016..14683622976...710001723456...34589078037504

.589824.40310784.2754990144.200937920832.14819050600704.1104253773912576

Examples

			Some solutions for n=5 k=3
..0..1..0..1....1..2..0..1....0..1..2..1....2..2..0..1....2..2..2..1
..2..1..2..1....1..2..0..1....2..1..0..0....0..1..0..2....0..0..0..1
..0..0..0..1....1..2..0..2....2..1..2..1....2..1..0..1....2..2..2..2
..1..1..2..1....1..2..0..1....2..0..2..0....2..1..2..2....0..0..0..1
..0..0..2..0....1..2..0..1....1..0..2..0....0..0..0..0....2..2..2..2
..1..1..1..1....0..2..0..1....1..0..1..1....1..2..1..2....1..0..0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..285

Crossrefs

Column 1 is A002063

Column 2 is A067411(n+2)

Column 3 is A055995(n+2)

Formula

Empirical for column k:

k=1: T(n,k)=4*T(n-1,k)

k=2: T(n,k)=6*T(n-1,k)

k=3: T(n,k)=9*T(n-1,k)

k=4: T(n,k)=15*T(n-1,k)-270*T(n-3,k)+324*T(n-4,k)

k=5: T(n,k)=25*T(n-1,k)-45*T(n-2,k)-963*T(n-3,k)+2025*T(n-4,k)+3645*T(n-5,k)-6561*T(n-6,k)

k=6: (order 15)

k=7: (order 45)