A297802 T(n,k) = Number of n X k 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 5 neighboring 1's.

1, 1, 1, 1, 2, 1, 1, 11, 4, 1, 1, 24, 37, 7, 1, 1, 38, 100, 108, 14, 1, 1, 105, 293, 422, 533, 31, 1, 1, 381, 1320, 2195, 2936, 2434, 69, 1, 1, 1067, 6215, 16006, 23781, 17899, 10287, 155, 1, 1, 2676, 24879, 115773, 320168, 231921, 104985, 45968, 354, 1, 1, 7533, 99567

Offset: 1

Author

R. H. Hardin, Jan 06 2018

Keywords

• nonn
• tabl

Comments

Table starts

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

.1...2.....11......24........38.........105...........381............1067

.1...4.....37.....100.......293........1320..........6215...........24879

.1...7....108.....422......2195.......16006........115773..........738989

.1..14....533....2936.....23781......320168.......4340367........46828204

.1..31...2434...17899....231921.....5511367.....123361724......2122878239

.1..69..10287..104985...2174696....91376524....3420197908.....94927605755

.1.155..45968..645568..21427001..1587468720..102189481612...4611250894511

.1.354.207906.3978117.209042911.27421636815.2993486726263.218072722004943

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..180

Crossrefs

Column 2 is A202973.

Row 2 is A297545.

Formula

Empirical for column k:

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

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

k=3: [order 15],

k=4: [order 37],

k=5: [order 95].

Empirical for row n:

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

n=2: a(n) = 3*a(n-1) -2*a(n-2) +5*a(n-3) +6*a(n-4) -16*a(n-5) -12*a(n-6),

n=3: [order 21],

n=4: [order 55].