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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
13
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Dec 18 2012
STATUS
approved