A220621 T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly one horizontal, diagonal and antidiagonal neighbor

1, 2, 1, 3, 7, 1, 5, 21, 22, 1, 8, 87, 125, 71, 1, 13, 317, 1189, 765, 228, 1, 21, 1215, 9176, 17084, 4657, 733, 1, 34, 4565, 76955, 282777, 243119, 28373, 2356, 1, 55, 17287, 624227, 5280827, 8608738, 3466455, 172833, 7573, 1, 89, 65261, 5131406, 93905509

Offset

1,2

Comments

Table starts

.1......2..........3..............5..................8.....................13

.1......7.........21.............87................317...................1215

.1.....22........125...........1189...............9176..................76955

.1.....71........765..........17084.............282777................5280827

.1....228.......4657.........243119............8608738..............356768525

.1....733......28373........3466455..........262680517............24177895648

.1...2356.....172833.......49406943.........8011414792..........1637496710797

.1...7573....1052829......704243629.......244357686173........110916199227139

.1..24342....6413369....10038098456......7453056468816.......7512747980759983

.1..78243...39067429...143080761421....227323314349577.....508867505795261823

.1.251498..237981569..2039439299333...6933510501158596...34467532553765146717

.1.808395.1449678893.29069688249415.211476640729594693.2334617570886588879553

Links

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

Example

Some solutions for n=3 k=4 0=self 1=nw 3=ne 4=w 6=e 7=sw 9=se (reciprocal directions total 10)
..6..4..6..4....9..9..6..4....6..4..9..7....6..4..6..4....6..4..6..4
..0..7..6..4....0..1..1..0....0..0..3..1....0..0..7..0....0..6..4..0
..3..6..4..0....6..4..0..0....0..6..4..0....0..3..6..4....6..4..6..4

Crossrefs

Column 2 is A030186

Row 1 is A000045(n+1)

Row 2 is A177369

Sequence in context: A116381 A176120 A369595 * A360587 A058170 A238206

Adjacent sequences: A220618 A220619 A220620 * A220622 A220623 A220624

Keyword

nonn,tabl

Author

R. H. Hardin Dec 17 2012

Status

approved