A281802 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

0, 1, 0, 0, 0, 0, 3, 6, 9, 0, 3, 38, 75, 34, 0, 9, 157, 372, 324, 87, 0, 15, 524, 1725, 1916, 865, 194, 0, 31, 1631, 7293, 12318, 8354, 2272, 400, 0, 57, 4694, 29665, 71290, 71445, 32524, 5191, 790, 0, 108, 13006, 116539, 396185, 575062, 368408, 117401, 11141

Offset: 1

Author

R. H. Hardin, Jan 30 2017

Keywords

• nonn
• tabl

Comments

Table starts

.0....1.....0.......3.........3..........9...........15.............31

.0....0.....6......38.......157........524.........1631...........4694

.0....9....75.....372......1725.......7293........29665.........116539

.0...34...324....1916.....12318......71290.......396185........2143364

.0...87...865....8354.....71445.....575062......4480480.......33526931

.0..194..2272...32524....368408....4173476.....45696162......473403162

.0..400..5191..117401...1770697...28237876....436154254.....6282549989

.0..790.11141..404594...8100180..181908580...3971817891....79584142302

.0.1511.22705.1345667..35778250.1130079060..34908793027...974107985517

.0.2830.44611.4351562.153961577.6826668428.298606378335.11610933931800

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..161

Crossrefs

Column 2 is A279128.

Row 1 is A105423(n-2).

Formula

Empirical for column k:

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

k=2: [order 8] for n>9

k=3: [order 9] for n>16

k=4: [order 44] for n>51

k=5: [order 72] for n>86

Empirical for row n:

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

n=2: [order 14]

n=3: [order 60]