A304419 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 4, 1, 1, 8, 8, 1, 1, 24, 23, 24, 1, 1, 82, 103, 103, 82, 1, 1, 272, 520, 835, 520, 272, 1, 1, 908, 2671, 7017, 7017, 2671, 908, 1, 1, 3076, 13876, 60245, 98568, 60245, 13876, 3076, 1, 1, 10444, 72399, 522349, 1389257, 1389257, 522349, 72399, 10444, 1

Offset

1,5

Comments

Table starts

.1.....1......1........1..........1............1..............1

.1.....4......8.......24.........82..........272............908

.1.....8.....23......103........520.........2671..........13876

.1....24....103......835.......7017........60245.........522349

.1....82....520.....7017......98568......1389257.......19831472

.1...272...2671....60245....1389257.....32181958......755715475

.1...908..13876...522349...19831472....755715475....29251894460

.1..3076..72399..4542604..283040177..17729422188..1129111647895

.1.10444.378321.39567170.4045732942.416850100691.43720181502419

Links

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

Formula

Empirical for column k:

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

k=2: a(n) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6

k=3: [order 15] for n>17

k=4: [order 47] for n>48

Example

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

Crossrefs

Column 2 is A303882.

Sequence in context: A316376 A306136 A317271 * A316244 A305954 A317215

Adjacent sequences: A304416 A304417 A304418 * A304420 A304421 A304422

Keyword

nonn,tabl

Author

R. H. Hardin, May 12 2018

Status

approved