A316311 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 6 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 5, 3, 5, 7, 7, 5, 8, 17, 10, 17, 8, 13, 35, 21, 21, 35, 13, 21, 61, 44, 74, 44, 61, 21, 34, 127, 83, 148, 148, 83, 127, 34, 55, 265, 168, 404, 662, 404, 168, 265, 55, 89, 507, 365, 1046, 1488, 1488, 1046, 365, 507, 89, 144, 1013, 766, 3023, 4583, 4431, 4583

Offset

1,2

Comments

Table starts

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

..2...5...7...17....35.....61.....127......265.......507.......1013........2071

..3...7..10...21....44.....83.....168......365.......766.......1615........3490

..5..17..21...74...148....404....1046.....3023......8295......24149.......72052

..8..35..44..148...662...1488....4583....18558.....56204.....188141......712440

.13..61..83..404..1488...4431...17487....75221....293206....1262596.....5656690

.21.127.168.1046..4583..17487...96175...534083...2689151...15357780....89959730

.34.265.365.3023.18558..75221..534083..3854852..23640130..172324121..1280488352

.55.507.766.8295.56204.293206.2689151.23640130.190235425.1767871577.16603983388

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

Formula

Empirical for column k:

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

k=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) -4*a(n-4) for n>5

k=3: [order 16]

k=4: [order 67] for n>68

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A303802.

Sequence in context: A305482 A305252 A316552 * A317266 A067330 A202874

Adjacent sequences: A316308 A316309 A316310 * A316312 A316313 A316314

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 29 2018

Status

approved