A305649 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 5, 3, 5, 9, 9, 5, 8, 21, 13, 21, 8, 13, 57, 31, 31, 57, 13, 21, 125, 79, 137, 79, 125, 21, 34, 289, 168, 574, 574, 168, 289, 34, 55, 741, 430, 2360, 5547, 2360, 430, 741, 55, 89, 1737, 1241, 13498, 31079, 31079, 13498, 1241, 1737, 89, 144, 4045, 3577, 83190

Offset

1,2

Comments

Table starts

..1....2....3......5........8.........13...........21.............34

..2....5....9.....21.......57........125..........289............741

..3....9...13.....31.......79........168..........430...........1241

..5...21...31....137......574.......2360........13498..........83190

..8...57...79....574.....5547......31079.......304707........3821570

.13..125..168...2360....31079.....355620......7215825......146459610

.21..289..430..13498...304707....7215825....283691091....10435409852

.34..741.1241..83190..3821570..146459610..10435409852...724085314967

.55.1737.3577.481377.37230262.2640107792.345636487600.42678601156125

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) = 2*a(n-1) -a(n-2) +8*a(n-3) -8*a(n-4)

k=3: [order 17] for n>19

k=4: [order 54] for n>57

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A304349.

Sequence in context: A306172 A304355 A305918 * A316925 A305347 A316615

Adjacent sequences: A305646 A305647 A305648 * A305650 A305651 A305652

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 07 2018

Status

approved