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

1,2

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

Links

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

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]

Example

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

Crossrefs

Column 2 is A105309(n+1).

Row 1 is A000930(n+1).

Sequence in context: A118243 A210233 A347667 * A134081 A134247 A210225

Adjacent sequences: A297579 A297580 A297581 * A297583 A297584 A297585

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 01 2018

Status

approved