A269097 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.

0, 4, 4, 24, 96, 24, 108, 1152, 1152, 108, 432, 11424, 31296, 11424, 432, 1620, 103488, 715320, 715320, 103488, 1620, 5832, 889056, 15024096, 37963968, 15024096, 889056, 5832, 20412, 7375872, 300056400, 1856325000, 1856325000, 300056400, 7375872

Offset

1,2

Comments

Table starts

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

......4.........96...........1152..............11424.................103488

.....24.......1152..........31296.............715320...............15024096

....108......11424.........715320...........37963968.............1856325000

....432.....103488.......15024096.........1856325000...........211625837280

...1620.....889056......300056400........86415197088.........22984646281176

...5832....7375872.....5795398368......3892946216856.......2416707037884480

..20412...59698464...109294975080....171307237216320.....248267055360211392

..69984..474360768..2024660774592...7406621052177000...25062609875880382656

.236196.3715826016.36988673403168.315868041326151072.2495854741014485439624

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

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

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

k=3: a(n) = 36*a(n-1) -378*a(n-2) +972*a(n-3) -729*a(n-4) for n>5

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

k=5: [order 14] for n>15

k=6: [order 26] for n>27

k=7: [order 64] for n>65

Example

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

Crossrefs

Column 1 is A120908.

Sequence in context: A058166 A092897 A269152 * A307552 A171633 A221276

Adjacent sequences: A269094 A269095 A269096 * A269098 A269099 A269100

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 19 2016

Status

approved