A318545 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 3, 1, 3, 5, 3, 3, 5, 8, 5, 6, 5, 8, 13, 8, 13, 13, 8, 13, 21, 15, 26, 31, 26, 15, 21, 34, 26, 52, 78, 78, 52, 26, 34, 55, 45, 107, 207, 247, 207, 107, 45, 55, 89, 80, 218, 516, 784, 784, 516, 218, 80, 89, 144, 140, 442, 1288, 2349, 2905, 2349, 1288, 442, 140, 144, 233

Offset: 1

Author

R. H. Hardin, Aug 28 2018

Keywords

• nonn
• tabl

Comments

Table starts

..1..2...3....5.....8.....13.....21......34.......55........89........144

..2..1...3....5.....8.....15.....26......45.......80.......140........245

..3..3...6...13....26.....52....107.....218......442.......899.......1829

..5..5..13...31....78....207....516....1288.....3270......8271......20866

..8..8..26...78...247....784...2349....7191....22268.....68384.....210050

.13.15..52..207...784...2905..10496...38721...144148....531780....1960675

.21.26.107..516..2349..10496..46165..208159...942764...4213744...18870716

.34.45.218.1288..7191..38721.208159.1143583..6263377..33963639..184912113

.55.80.442.3270.22268.144148.942764.6263377.41368803.271753441.1792754281

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..924

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A193147.

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = a(n-1) +2*a(n-3) +a(n-5) for n>6

k=3: a(n) = a(n-1) +3*a(n-3) +a(n-4) +3*a(n-5) +a(n-7) for n>8

k=4: [order 13] for n>14

k=5: [order 23] for n>24

k=6: [order 37] for n>38

k=7: [order 63] for n>64