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

1,1

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

Links

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

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)

Example

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

Crossrefs

Column 1 is A002063

Column 2 is A067411(n+2)

Column 3 is A055995(n+2)

Sequence in context: A303899 A245530 A138202 * A049227 A368682 A016910

Adjacent sequences: A204103 A204104 A204105 * A204107 A204108 A204109

Keyword

nonn,tabl

Author

R. H. Hardin Jan 10 2012

Status

approved