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

Author

R. H. Hardin, Feb 20 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A120926(n+1).

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