A297544 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 or 3 neighboring 1s.

1, 1, 1, 1, 2, 1, 1, 11, 4, 1, 1, 24, 35, 7, 1, 1, 38, 93, 88, 14, 1, 1, 105, 197, 275, 461, 31, 1, 1, 381, 905, 1233, 2205, 2050, 69, 1, 1, 1067, 4617, 10234, 12161, 13248, 8057, 155, 1, 1, 2676, 17190, 65363, 205888, 94647, 67215, 35640, 354, 1, 1, 7533, 60751, 355573

Offset: 1

Author

R. H. Hardin, Dec 31 2017

Keywords

• nonn
• tabl

Comments

Table starts

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

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

.1...4.....35......93......197.........905..........4617..........17190

.1...7.....88.....275.....1233.......10234.........65363.........355573

.1..14....461....2205....12161......205888.......2748026.......25141813

.1..31...2050...13248....94647.....3015179......67372651......916902295

.1..69...8057...67215...754342....45293985....1610981344....33425081735

.1.155..35640..401415..6315609...726450667...45496070039..1479214192234

.1.354.158090.2403621.51451261.11267743659.1204223924807.59920115456355

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..199

Crossrefs

Column 2 is A202973.

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 14]

k=4: [order 22]

k=5: [order 54]

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 17]

n=4: [order 40]