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%I #4 Dec 18 2012 12:49:37
%S 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,
%T 1,1,221,2276,7369,5760,949,64,1,1,578,10653,78418,127288,45421,3403,
%U 128,1,1,1513,49951,824965,2792479,2027456,355883,12241,256,1,1,3961,234006
%N 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
%C Table starts
%C .1....1.......1...........1.............1...............1................1
%C .1....2.......5..........13............32..............85..............221
%C .1....4......22.........103...........487............2276............10653
%C .1....8......72.........712..........7369...........78418...........824965
%C .1...16.....258........5760........127288.........2792479.........60293428
%C .1...32.....949.......45421.......2027456........94226589.......4335687696
%C .1...64....3403......355883......32924133......3287610473.....319803318494
%C .1..128...12241.....2807273.....534490260....113721332657...23223803317197
%C .1..256...44192....22112517....8661108365...3938053379575.1694411878011549
%C .1..512..159272...174154372..140500900684.136391275221050
%C .1.1024..573952..1371967416.2278575841968
%C .1.2048.2069009.10807412577
%H R. H. Hardin, <a href="/A220738/b220738.txt">Table of n, a(n) for n = 1..126</a>
%e 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)
%e .00.69.49.00...00.69.47.00...00.00.69.47...00.79.79.00...00.00.79.00
%e .00.00.16.14...00.36.14.00...00.00.36.14...39.39.17.17...00.39.67.14
%e .00.00.00.00...00.00.00.00...00.00.00.00...00.13.13.00...00.36.14.00
%Y Column 2 is A000079(n-1)
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_ Dec 18 2012
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