A316244 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4, 5 or 8 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, 99193, 60245, 13876, 3076, 1, 1, 10444, 72399, 522349, 1402577, 1402577, 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......99193......1402577.......20134728

.1...272...2671....60245....1402577.....32646098......772981023

.1...908..13876...522349...20134728....772981023....30308496367

.1..3076..72399..4542604..288724218..18258025708..1182294908774

.1.10444.378321.39567170.4148322120.432527550123.46316454084857

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..1..0. .0..1..0..1. .0..0..1..0. .0..1..0..0. .0..1..0..1
..0..1..1..0. .1..1..1..0. .1..1..1..1. .1..1..1..1. .1..1..1..0
..0..0..0..0. .0..0..1..0. .0..1..0..0. .1..0..0..0. .0..0..0..0
..1..0..0..1. .0..0..1..1. .1..0..0..1. .0..0..0..0. .1..1..0..1
..1..0..0..1. .1..1..1..0. .0..1..0..1. .1..0..1..1. .1..1..0..1

Crossrefs

Column 2 is A303882.

Column 3 is A304414.

Column 4 is A304415.

Sequence in context: A306136 A317271 A304419 * A305954 A317215 A305685

Adjacent sequences: A316241 A316242 A316243 * A316245 A316246 A316247

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 27 2018

Status

approved