login
A302224
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
13
0, 1, 0, 1, 3, 0, 2, 14, 11, 0, 3, 45, 43, 34, 0, 5, 146, 164, 194, 111, 0, 8, 537, 760, 934, 675, 361, 0, 13, 1934, 3425, 6110, 4237, 2666, 1172, 0, 21, 6861, 15569, 38736, 40395, 21777, 9819, 3809, 0, 34, 24386, 70323, 251254, 338204, 292781, 105585, 37382
OFFSET
1,5
COMMENTS
Table starts
.0.....1......1.......2.........3..........5...........8............13
.0.....3.....14......45.......146........537........1934..........6861
.0....11.....43.....164.......760.......3425.......15569.........70323
.0....34....194.....934......6110......38736......251254.......1610569
.0...111....675....4237.....40395.....338204.....3018243......26373655
.0...361...2666...21777....292781....3420704....42508145.....524715109
.0..1172...9819..105585...2043848...32181643...553097760....9458629708
.0..3809..37382..523414..14419536..310963650..7403262824..177191137344
.0.12377.140039.2578424.101511446.2973099477.97939043966.3265007473096
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
k=3: [order 11]
k=4: [order 30] for n>34
k=5: [order 92] for n>97
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) +3*a(n-2) +6*a(n-3) +10*a(n-4) +4*a(n-5) for n>6
n=3: [order 15] for n>17
n=4: [order 54] for n>58
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..1. .0..0..1..0. .0..0..1..1. .0..0..0..1. .0..0..1..1
..0..1..1..1. .1..1..0..1. .0..1..0..1. .1..1..1..0. .0..1..1..1
..1..0..0..0. .1..1..0..0. .1..0..0..1. .0..0..0..0. .1..0..0..0
..1..1..1..1. .1..0..0..1. .1..1..1..1. .0..1..1..1. .0..0..1..1
..0..0..0..0. .1..1..1..0. .0..0..0..0. .0..0..1..1. .0..0..1..1
CROSSREFS
Column 2 is A180762.
Row 1 is A000045(n-1).
Sequence in context: A256548 A239098 A319501 * A302670 A302472 A303254
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 03 2018
STATUS
approved