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

1,7

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

Links

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

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]

Example

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

Crossrefs

Column 2 is A279128.

Row 1 is A105423(n-2).

Sequence in context: A103268 A114157 A021275 * A197292 A232817 A346640

Adjacent sequences: A281799 A281800 A281801 * A281803 A281804 A281805

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 30 2017

Status

approved