A220632 T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal or antidiagonal neighbors

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 1, 8, 12, 5, 1, 1, 1, 16, 44, 37, 8, 1, 1, 1, 32, 158, 257, 114, 13, 1, 1, 1, 64, 564, 1665, 1481, 351, 21, 1, 1, 1, 128, 2010, 10695, 17527, 8560, 1081, 34, 1, 1, 1, 256, 7160, 68637, 201903, 183961, 49448, 3329, 55, 1, 1, 1, 512

Offset

1,8

Comments

Table starts

.1.1...1......1.........1............1...............1..................1

.1.1...2......4.........8...........16..............32.................64

.1.1...3.....12........44..........158.............564...............2010

.1.1...5.....37.......257.........1665...........10695..............68637

.1.1...8....114......1481........17527..........201903............2329448

.1.1..13....351......8560.......183961.........3817452...........79063898

.1.1..21...1081.....49448......1932695........72097810.........2685329069

.1.1..34...3329....285669.....20301254......1362188752........91163971015

.1.1..55..10252...1650333....213251377.....25734606523......3095401422320

.1.1..89..31572...9534128...2240062837....486186026515....105098157017450

.1.1.144..97229..55079528..23530357757...9185167500820...3568417528948249

.1.1.233.299426.318199485.247170637157.173528846174065.121159087987547537

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

Example

Some solutions for n=3 k=4 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)
.00.67.46.47...00.67.46.47...00.67.47.00...00.00.00.00...00.00.67.47
.36.46.34.00...36.47.36.47...36.34.00.00...00.00.00.00...00.37.36.47
.00.00.00.00...36.46.34.00...00.00.00.00...00.00.00.00...36.46.34.00

Crossrefs

Column 3 is A000045(n+1)

Column 4 is A099098

Row 2 is A000079(n-2)

Sequence in context: A327502 A354090 A362826 * A125653 A104445 A359762

Adjacent sequences: A220629 A220630 A220631 * A220633 A220634 A220635

Keyword

nonn,tabl

Author

R. H. Hardin Dec 17 2012

Status

approved