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

1,2

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

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: 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

Example

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

Crossrefs

Column 2 is A269091.

Row 1 is A120908.

Sequence in context: A329891 A357810 A057402 * A269276 A359521 A172394

Adjacent sequences: A269211 A269212 A269213 * A269215 A269216 A269217

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 20 2016

Status

approved