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.

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

R. H. Hardin, Table of n, a(n) for n = 1..181

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: A239098 A319501 A379578 * A302670 A302472 A303254

Adjacent sequences: A302221 A302222 A302223 * A302225 A302226 A302227

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 03 2018

Status

approved