A228754 T(n,k)=Number of nXk binary arrays with top left element equal to 1 and no two ones adjacent horizontally or antidiagonally.

1, 1, 2, 2, 3, 4, 3, 9, 8, 8, 5, 20, 39, 21, 16, 8, 50, 126, 168, 55, 32, 13, 119, 482, 780, 723, 144, 64, 21, 289, 1712, 4599, 4808, 3111, 377, 128, 34, 696, 6277, 24246, 43862, 29608, 13386, 987, 256, 55, 1682, 22700, 134440, 342207, 418370, 182288, 57597, 2584, 512

Offset: 1

Author

R. H. Hardin Sep 02 2013

Keywords

• nonn
• tabl

Comments

Table starts

...1....1......2.......3.........5...........8...........13.............21

...2....3......9......20........50.........119..........289............696

...4....8.....39.....126.......482........1712.........6277..........22700

...8...21....168.....780......4599.......24246.......134440.........728537

..16...55....723....4808.....43862......342207......2876170.......23326164

..32..144...3111...29608....418370.....4823826.....61534448......746135864

..64..377..13386..182288...3990739....67970044...1316714732....23857469157

.128..987..57597.1122240..38067290...957616341..28177227352...762713002760

.256.2584.247827.6908896.363121586.13491214832.602998827928.24382157716612

Examples

			Some solutions for n=4 k=4
..1..0..1..0....1..0..0..1....1..0..0..0....1..0..0..1....1..0..1..0
..0..0..0..1....1..0..0..0....1..0..0..0....0..1..0..0....1..0..0..1
..0..0..0..0....1..0..0..1....0..0..0..0....0..0..0..1....0..1..0..1
..0..0..0..1....0..0..0..0....0..1..0..0....0..1..0..0....0..0..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1347

Crossrefs

Column 1 is A000079(n-1)

Column 2 is A001906

Column 3 is A095939

Row 1 is A000045

Row 2 is A097075(n+1)

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

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

k=3: a(n) = 5*a(n-1) -3*a(n-2)

k=4: a(n) = 8*a(n-1) -12*a(n-2) +4*a(n-3)

k=5: a(n) = 13*a(n-1) -36*a(n-2) +29*a(n-3) -5*a(n-4) for n>5

k=6: a(n) = 21*a(n-1) -112*a(n-2) +217*a(n-3) -157*a(n-4) +36*a(n-5) for n>6

k=7: [order 7] for n>9

Empirical for row n:

n=1: a(n) = a(n-1) +a(n-2)

n=2: a(n) = a(n-1) +3*a(n-2) +a(n-3)

n=3: a(n) = 2*a(n-1) +6*a(n-2) -a(n-4)

n=4: [order 8]

n=5: [order 13]

n=6: [order 21]

n=7: [order 34]