A203732 T(n,k)=Number of (n+1)X(k+1) 0..7 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements

960, 14400, 14400, 216000, 539456, 216000, 3240000, 19071424, 19071424, 3240000, 48600000, 681461824, 1754118528, 681461824, 48600000, 729000000, 24301391808, 161916229056, 161916229056, 24301391808, 729000000, 10935000000

Offset

1,1

Comments

Table starts

..........960..........14400...........216000..........3240000.........48600000

........14400.........539456.........19071424........681461824......24301391808

.......216000.......19071424.......1754118528.....161916229056...14950234495680

......3240000......681461824.....161916229056...39986164706496.9889622728751424

.....48600000....24301391808...14950234495680.9889622728751424

....729000000...866928276544.1380434809882752

..10935000000.30924651270080

.164025000000

Links

R. H. Hardin, Table of n, a(n) for n = 1..40

Formula

Empirical for column k:

k=1: a(n) = 64*15^n

k=2: a(n) = 29*a(n-1) +238*a(n-2)

k=3: a(n) = 99*a(n-1) -609*a(n-2) -588*a(n-3)

k=4: a(n) = 141*a(n-1) +34391*a(n-2) -1914087*a(n-3) -5360404*a(n-4) +185626112*a(n-5) +226020536*a(n-6) -801895584*a(n-7)

Example

Some solutions for n=4 k=3
..4..0..2..1....2..3..7..4....0..4..1..2....3..2..0..1....4..7..7..3
..1..4..0..2....4..2..3..7....0..0..4..1....0..3..2..0....2..4..7..7
..0..1..4..0....6..4..2..3....5..0..0..4....7..0..3..2....0..2..4..7
..2..0..1..4....6..6..4..2....1..5..0..0....1..7..0..3....3..0..2..4
..5..2..0..1....1..6..6..4....5..0..3..0....5..1..7..0....7..3..0..2

Crossrefs

Sequence in context: A057666 A046788 A206079 * A157851 A278011 A282012

Adjacent sequences: A203729 A203730 A203731 * A203733 A203734 A203735

Keyword

nonn,tabl

Author

R. H. Hardin Jan 05 2012

Status

approved