A269214 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.

0, 4, 0, 24, 96, 0, 108, 768, 1152, 0, 432, 6528, 18048, 11424, 0, 1620, 49536, 308544, 361728, 103488, 0, 5832, 360960, 4744704, 12548544, 6712704, 889056, 0, 20412, 2546304, 70371048, 394072704, 474091776, 118872576, 7375872, 0, 69984, 17563392

Offset: 1

Author

R. H. Hardin, Feb 20 2016

Keywords

• nonn
• tabl

Comments

Table starts

.0........4..........24............108...............432................1620

.0.......96.........768...........6528.............49536..............360960

.0.....1152.......18048.........308544...........4744704............70371048

.0....11424......361728.......12548544.........394072704.........11985002256

.0...103488.....6712704......474091776.......30541426560.......1910809190712

.0...889056...118872576....17118725376.....2267772823680.....292321215814512

.0..7375872..2039727744...599456856000...163535201141376...43468685827935816

.0.59698464.34214296320.20531285093184.11544796423498368.6331185189881558208

Examples

			Some solutions for n=3 k=4
..2..2..3..2. .2..2..2..3. .0..1..0..2. .0..0..0..2. .2..2..0..0
..0..2..0..2. .0..0..1..0. .1..1..3..0. .0..1..2..0. .0..0..2..3
..2..1..0..1. .0..1..0..1. .0..1..0..2. .0..0..0..0. .0..0..1..3
		

Links

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

Crossrefs

Column 2 is A269091.

Row 1 is A120908.

Formula

Empirical for column k:

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

k=2: a(n) = 14*a(n-1) -49*a(n-2) for n>3

k=3: a(n) = 30*a(n-1) -237*a(n-2) +180*a(n-3) -36*a(n-4) for n>5

k=4: [order 6] for n>7

k=5: [order 20] for n>21

k=6: [order 42] for n>43

Empirical for row n:

n=1: a(n) = 6*a(n-1) -9*a(n-2)

n=2: a(n) = 10*a(n-1) -13*a(n-2) -60*a(n-3) -36*a(n-4)

n=3: [order 8]

n=4: [order 20]

n=5: [order 52] for n>53