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

Author

R. H. Hardin Dec 17 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 3 is A000045(n+1)

Column 4 is A099098

Row 2 is A000079(n-2)