A240783 T(n,k)=Number of nXk 0..1 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..1 introduced in row major order.

1, 1, 2, 1, 3, 4, 1, 4, 11, 8, 1, 6, 20, 34, 16, 1, 9, 46, 97, 111, 32, 1, 14, 97, 305, 459, 361, 64, 1, 22, 216, 959, 2167, 2187, 1172, 128, 1, 35, 472, 3033, 10150, 15332, 10442, 3809, 256, 1, 56, 1043, 9581, 47920, 106411, 108509, 49861, 12377, 512, 1, 90, 2296, 30354

Offset: 1

Author

R. H. Hardin, Apr 12 2014

Keywords

• nonn
• tabl

Comments

Table starts

...1.....1.......1........1..........1...........1.............1..............1

...2.....3.......4........6..........9..........14............22.............35

...4....11......20.......46.........97.........216...........472...........1043

...8....34......97......305........959........3033..........9581..........30354

..16...111.....459.....2167......10150.......47920........226532........1071982

..32...361....2187....15332.....106411......746346.......5228820.......36701371

..64..1172...10442...108509....1120383....11677893.....121621207.....1269199948

.128..3809...49861...767834...11791412...182610635....2827515311....43857418181

.256.12377..238068..5434887..124095989..2856212777...65742420202..1515928067679

.512.40218.1136678.38467875.1306056075.44672652785.1528546759636.52397680462958

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..264

Crossrefs

Column 1 is A000079(n-1)

Column 2 is A180762

Row 2 is A001611(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) -2*a(n-4)

k=3: a(n) = 5*a(n-1) -a(n-2) -a(n-3) +4*a(n-4) -4*a(n-5) -3*a(n-6) +a(n-7)

k=4: [order 22]

k=5: [order 54]

Empirical for row n:

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

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

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

n=4: [order 15]

n=5: [order 30] for n>34

n=6: [order 94]