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

Author

R. H. Hardin, Apr 03 2018

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 2 is A180762.

Row 1 is A000045(n-1).

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