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

1,3

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A000079(n-1)

Column 2 is A180762

Row 2 is A001611(n+1)

Sequence in context: A159856 A137649 A180915 * A327083 A104002 A073135

Adjacent sequences: A240780 A240781 A240782 * A240784 A240785 A240786

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 12 2014

Status

approved