A303254 T(n,k) = Number of n X k 0..1 arrays with every element equal to 1, 2, 3, 5 or 6 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, 1183, 361, 0, 13, 1934, 4556, 10264, 8664, 5918, 1172, 0, 21, 6861, 21843, 78679, 106803, 55624, 28680, 3809, 0, 34, 24386, 103319, 584333, 1218385, 1105676, 349273

Offset: 1

Author

R. H. Hardin, Apr 20 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...1183.....8664.....106803.....1218385......13529019.......153269484

.0...361...5918....55624....1105676....19457754.....322544617......5622650429

.0..1172..28680...349273...11394429...306224454....7600681910....204093228252

.0..3809.141255..2229806..118856245..4895684572..181926316054...7516309079483

.0.12377.691968.14141138.1230109648.77683246701.4319287740641.274539947294004

Examples

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

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.

Row 3 is A302473.

Row 4 is A302474.

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