A269143 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

4, 16, 16, 60, 148, 60, 216, 1164, 1164, 216, 756, 8532, 18556, 8532, 756, 2592, 59916, 275796, 275796, 59916, 2592, 8748, 408596, 3924212, 8317996, 3924212, 408596, 8748, 29160, 2727564, 54199284, 240647068, 240647068, 54199284, 2727564, 29160

Offset

1,1

Comments

Table starts

......4........16............60..............216.................756

.....16.......148..........1164.............8532...............59916

.....60......1164.........18556...........275796.............3924212

....216......8532........275796..........8317996...........240647068

....756.....59916.......3924212........240647068.........14197016484

...2592....408596......54199284.......6766301156........815458664276

...8748...2727564.....732561916.....186315931804......45920055321732

..29160..17914580....9740150372....5049212790572....2546667557472940

..96228.116170764..127846717716..135126561336764..139535357045338964

.314928.745617300.1660741102212.3579710280903028.7570570235882777884

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

k=2: a(n) = 12*a(n-1) -38*a(n-2) +12*a(n-3) -a(n-4) for n>5

k=3: [order 8] for n>9

k=4: [order 20] for n>22

k=5: [order 42] for n>45

Example

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

Crossrefs

Column 1 is A120926(n+1).

Sequence in context: A207479 A207535 A269194 * A269109 A269201 A269289

Adjacent sequences: A269140 A269141 A269142 * A269144 A269145 A269146

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 20 2016

Status

approved