A283572 T(n,k) = Number of n X k 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.

0, 0, 0, 1, 4, 0, 2, 26, 16, 0, 5, 72, 169, 68, 0, 12, 282, 674, 1108, 256, 0, 26, 908, 4313, 6812, 6453, 924, 0, 56, 2832, 21186, 67892, 60802, 36038, 3232, 0, 118, 8856, 104464, 509952, 945100, 528436, 194173, 11044, 0, 244, 26750, 513458, 3890056, 10919674

Offset: 1

Author

R. H. Hardin, Mar 11 2017

Keywords

• nonn
• tabl

Comments

Table starts

.0......0........1..........2............5.............12...............26

.0......4.......26.........72..........282............908.............2832

.0.....16......169........674.........4313..........21186...........104464

.0.....68.....1108.......6812........67892.........509952..........3890056

.0....256.....6453......60802.......945100.......10919674........129527524

.0....924....36038.....528436.....12699250......226897932.......4173039716

.0...3232...194173....4441052....164714523.....4558585174.....129997769458

.0..11044..1021432...36589848...2089140956....89724600000....3965206666608

.0..37104..5275885..296555892..26034179747..1736716820366..118919078661476

.0.122984.26869458.2373574616.320066184088.33188681249924.3520469545329364

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..241

Crossrefs

Column 2 is A283036.

Row 1 is A073778(n-1).

Formula

Empirical for column k:

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

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

k=3: [order 12]

k=4: [order 16]

k=5: [order 42]

k=6: [order 54]

Empirical for row n:

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

n=2: a(n) = 2*a(n-1) +5*a(n-2) +2*a(n-3) -17*a(n-4) -24*a(n-5) -16*a(n-6)

n=3: [order 12]

n=4: [order 16]

n=5: [order 42]

n=6: [order 64]