A316383 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 6 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 23, 23, 2, 3, 86, 83, 86, 3, 5, 313, 464, 464, 313, 5, 8, 1145, 2280, 3909, 2280, 1145, 8, 13, 4184, 11423, 29877, 29877, 11423, 4184, 13, 21, 15293, 57453, 228485, 353009, 228485, 57453, 15293, 21, 34, 55895, 288496, 1755475, 4067961

Offset

1,5

Comments

Table starts

..0.....1.......1.........2..........3............5..............8

..1.....7......23........86........313.........1145...........4184

..1....23......83.......464.......2280........11423..........57453

..2....86.....464......3909......29877.......228485........1755475

..3...313....2280.....29877.....353009......4067961.......47958446

..5..1145...11423....228485....4067961.....70282175.....1244767536

..8..4184...57453...1755475...47958446...1244767536....33482107028

.13.15293..288496..13526926..564507777..22077180053...901574650029

.21.55895.1447883.103864609.6610746658.388558892008.24039453398630

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) +a(n-2)

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

k=3: [order 15] for n>16

k=4: [order 50] for n>51

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A303890.

Sequence in context: A304901 A316583 A304597 * A306143 A317376 A304427

Adjacent sequences: A316380 A316381 A316382 * A316384 A316385 A316386

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 30 2018

Status

approved