A220738 T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal, diagonal and antidiagonal neighbors, without consecutive collinear links

1, 1, 1, 1, 2, 1, 1, 5, 4, 1, 1, 13, 22, 8, 1, 1, 32, 103, 72, 16, 1, 1, 85, 487, 712, 258, 32, 1, 1, 221, 2276, 7369, 5760, 949, 64, 1, 1, 578, 10653, 78418, 127288, 45421, 3403, 128, 1, 1, 1513, 49951, 824965, 2792479, 2027456, 355883, 12241, 256, 1, 1, 3961, 234006

Offset

1,5

Comments

Table starts

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

.1....2.......5..........13............32..............85..............221

.1....4......22.........103...........487............2276............10653

.1....8......72.........712..........7369...........78418...........824965

.1...16.....258........5760........127288.........2792479.........60293428

.1...32.....949.......45421.......2027456........94226589.......4335687696

.1...64....3403......355883......32924133......3287610473.....319803318494

.1..128...12241.....2807273.....534490260....113721332657...23223803317197

.1..256...44192....22112517....8661108365...3938053379575.1694411878011549

.1..512..159272...174154372..140500900684.136391275221050

.1.1024..573952..1371967416.2278575841968

.1.2048.2069009.10807412577

Links

R. H. Hardin, Table of n, a(n) for n = 1..126

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)
.00.69.49.00...00.69.47.00...00.00.69.47...00.79.79.00...00.00.79.00
.00.00.16.14...00.36.14.00...00.00.36.14...39.39.17.17...00.39.67.14
.00.00.00.00...00.00.00.00...00.00.00.00...00.13.13.00...00.36.14.00

Crossrefs

Column 2 is A000079(n-1)

Sequence in context: A263294 A241500 A152924 * A284732 A371766 A327483

Adjacent sequences: A220735 A220736 A220737 * A220739 A220740 A220741

Keyword

nonn,tabl

Author

R. H. Hardin Dec 18 2012

Status

approved