login
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.
8
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 20 2016
STATUS
approved