A297314 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 or 2 neighboring 1s.

1, 2, 1, 4, 7, 1, 7, 23, 21, 1, 12, 66, 117, 65, 1, 21, 207, 497, 609, 200, 1, 37, 654, 2577, 3808, 3159, 616, 1, 65, 2049, 13937, 35476, 29212, 16389, 1897, 1, 114, 6422, 72541, 340825, 484808, 223995, 85041, 5842, 1, 200, 20119, 375054, 2997197, 8273245

Offset

1,2

Comments

Table starts

.1.....2.......4.........7..........12............21..............37

.1.....7......23........66.........207...........654............2049

.1....21.....117.......497........2577.........13937...........72541

.1....65.....609......3808.......35476........340825.........2997197

.1...200....3159.....29212......484808.......8273245.......121339476

.1...616...16389....223995.....6623719.....200646607......4893232934

.1..1897...85041...1717882....90535227....4869858862....197589351469

.1..5842..441225..13174266..1237278512..118156684121...7976248015498

.1.17991.2289339.101033369.16909630099.2867120332406.322003901582689

Links

R. H. Hardin, Table of n, a(n) for n = 1..447

Formula

Empirical for column k:

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

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

k=3: a(n) = 3*a(n-1) +11*a(n-2) +3*a(n-3) -6*a(n-4)

k=4: [order 8] for n>9

k=5: [order 12] for n>14

k=6: [order 22] for n>25

k=7: [order 35] for n>39

Empirical for row n:

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

n=2: [order 9]

n=3: [order 23]

n=4: [order 61]

Example

Some solutions for n=5 k=4
..0..1..1..1. .1..1..0..0. .1..1..1..0. .0..1..0..0. .0..0..1..0
..1..0..0..0. .0..0..0..1. .0..0..1..0. .1..1..1..1. .1..1..0..0
..0..1..0..1. .0..0..1..0. .0..1..1..0. .0..0..0..1. .0..0..0..1
..1..1..1..0. .0..0..1..0. .0..1..0..0. .0..0..1..1. .0..1..1..0
..0..0..0..0. .0..1..1..1. .0..1..1..1. .0..0..1..1. .1..0..1..1

Crossrefs

Column 2 is A218836.

Row 1 is A005251(n+2).

Sequence in context: A193591 A218842 A219421 * A220386 A219410 A221035

Adjacent sequences: A297311 A297312 A297313 * A297315 A297316 A297317

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 28 2017

Status

approved