A316576 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 4, 1, 1, 8, 8, 1, 1, 24, 11, 24, 1, 1, 82, 40, 40, 82, 1, 1, 272, 94, 246, 94, 272, 1, 1, 908, 291, 899, 899, 291, 908, 1, 1, 3076, 776, 4262, 3180, 4262, 776, 3076, 1, 1, 10444, 2269, 18773, 17695, 17695, 18773, 2269, 10444, 1, 1, 35480, 6275, 86217

Offset

1,5

Comments

Table starts

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

.1.....4....8.....24......82......272.......908.......3076........10444

.1.....8...11.....40......94......291.......776.......2269.........6275

.1....24...40....246.....899.....4262.....18773......86217.......393045

.1....82...94....899....3180....17695.....88597.....457091......2402617

.1...272..291...4262...17695...129257....873130....5763068.....41285414

.1...908..776..18773...88597...873130...8469438...69549901....725190299

.1..3076.2269..86217..457091..5763068..69549901..730909482...9689842501

.1.10444.6275.393045.2402617.41285414.725190299.9689842501.185758559665

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

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 19] for n>20

k=4: [order 49] for n>52

Example

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

Crossrefs

Column 2 is A303882.

Column 3 is A304889.

Column 4 is A304890.

Sequence in context: A303888 A305281 A304894 * A304551 A316376 A306136

Adjacent sequences: A316573 A316574 A316575 * A316577 A316578 A316579

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 07 2018

Status

approved