A297582 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 4 neighboring 1s.

1, 2, 1, 3, 5, 1, 4, 11, 9, 1, 6, 17, 36, 20, 1, 9, 39, 72, 102, 41, 1, 13, 93, 188, 254, 370, 85, 1, 19, 183, 688, 1017, 1104, 1243, 178, 1, 28, 373, 2085, 5263, 5800, 4428, 3854, 369, 1, 41, 823, 5497, 20771, 47968, 31171, 17549, 13078, 769, 1, 60, 1741, 16037, 76340

Offset: 1

Author

R. H. Hardin, Jan 01 2018

Keywords

• nonn
• tabl

Comments

Table starts

.1...2.....3......4.......6.........9.........13..........19............28

.1...5....11.....17......39........93........183.........373...........823

.1...9....36.....72.....188.......688.......2085........5497.........16037

.1..20...102....254....1017......5263......20771.......76340........320326

.1..41...370...1104....5800.....47968.....284289.....1400065.......8274627

.1..85..1243...4428...31171....395011....3355439....21941552.....181405030

.1.178..3854..17549..171543...3230902...38609160...348140132....4059598106

.1.369.13078..71541..945046..27481626..476513137..5752782514...94310855136

.1.769.43861.288624.5175491.229676841.5731862594.92802629660.2136636243308

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..311

Crossrefs

Column 2 is A105309(n+1).

Row 1 is A000930(n+1).

Formula

Empirical for column k:

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

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

k=3: a(n) = a(n-1) +2*a(n-2) +19*a(n-3) +4*a(n-4) -17*a(n-5) -8*a(n-6)

k=4: [order 16]

k=5: [order 30]

k=6: [order 57]

Empirical for row n:

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

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

n=3: a(n) = a(n-1) +a(n-2) +8*a(n-3) +18*a(n-4) +a(n-5) -11*a(n-6) -12*a(n-7) -a(n-8)

n=4: [order 17]

n=5: [order 41]

n=6: [order 94]