A302472 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

0, 1, 0, 1, 3, 0, 2, 14, 11, 0, 3, 45, 49, 34, 0, 5, 146, 203, 250, 111, 0, 8, 537, 955, 1401, 1147, 361, 0, 13, 1934, 4556, 10264, 8493, 5486, 1172, 0, 21, 6861, 21843, 78679, 101109, 53575, 25599, 3809, 0, 34, 24386, 103319, 584333, 1141147, 990266, 331044

Offset: 1

Author

R. H. Hardin, Apr 08 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.....49......203.......955........4556.........21843..........103319

.0....34....250.....1401.....10264.......78679........584333.........4330427

.0...111...1147.....8493....101109.....1141147......12546601.......139759054

.0...361...5486....53575....990266....16983273.....278275383......4682106140

.0..1172..25599...331044...9731423...251512646....6145486847....156721340433

.0..3809.121626..2075845..96648626..3770915891..137317050228...5300304476103

.0.12377.572657.12918219.950374395.55956081186.3037409718914.177368160967073

Examples

			Some solutions for n=5 k=4
..0..1..0..1. .0..0..0..0. .0..1..1..1. .0..0..1..1. .0..0..1..1
..0..0..1..1. .1..1..1..0. .0..0..1..1. .0..1..0..1. .1..0..0..0
..1..1..1..1. .0..0..1..1. .1..1..0..1. .1..0..0..0. .1..1..1..1
..1..0..1..0. .1..0..0..0. .1..0..0..0. .0..1..0..1. .0..0..0..1
..0..0..0..1. .1..1..1..1. .1..1..1..0. .1..1..1..0. .1..1..1..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..180

Crossrefs

Column 2 is A180762.

Row 1 is A000045(n-1).

Row 2 is A302225.

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 14]

k=4: [order 43] for n>44

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 19] for n>21

n=4: [order 63] for n>66