A298133 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 5, 4, 5, 0, 0, 10, 13, 13, 10, 0, 0, 25, 62, 15, 62, 25, 0, 0, 54, 223, 233, 233, 223, 54, 0, 0, 125, 826, 1055, 2621, 1055, 826, 125, 0, 0, 282, 3200, 5782, 21537, 21537, 5782, 3200, 282, 0, 0, 641, 12098, 36225, 175014, 285084, 175014

Offset

1,8

Comments

Table starts

.0...0.....0......0........0.........0...........0.............0..............0

.0...1.....2......5.......10........25..........54...........125............282

.0...2.....4.....13.......62.......223.........826..........3200..........12098

.0...5....13.....15......233......1055........5782.........36225.........205348

.0..10....62....233.....2621.....21537......175014.......1557284.......13225388

.0..25...223...1055....21537....285084.....3752401......52922003......714854991

.0..54...826...5782...175014...3752401....76791444....1706951987....36185741209

.0.125..3200..36225..1557284..52922003..1706951987...58599163176..1933759163417

.0.282.12098.205348.13225388.714854991.36185741209.1933759163417.99650656591710

Links

R. H. Hardin, Table of n, a(n) for n = 1..197

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-2) +4*a(n-3) +2*a(n-4)

k=3: [order 18]

k=4: [order 53] for n>56

Example

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

Crossrefs

Column 2 is A297860.

Sequence in context: A245693 A370374 A297866 * A298070 A298719 A296148

Adjacent sequences: A298130 A298131 A298132 * A298134 A298135 A298136

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 13 2018

Status

approved