%I #4 Dec 16 2012 05:55:06

%S 1,89,1332,36640,810778,19333688,449429440,10536960271,246344047375,

%T 5764617097479,134855487893714,3155067573838299,73813420827751321,

%U 1726896241431387347,40401344327635974032,945204561717125804080

%N Number of ways to reciprocally link elements of an 5Xn array either to themselves or to exactly one horizontal or antidiagonal neighbor

%C Row 5 of A220562

%H R. H. Hardin, <a href="/A220566/b220566.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) +332*a(n-2) +1166*a(n-3) -10416*a(n-4) -41922*a(n-5) +174048*a(n-6) +535206*a(n-7) -1872086*a(n-8) -2804534*a(n-9) +11470692*a(n-10) +3617576*a(n-11) -32706416*a(n-12) +4049368*a(n-13) +51508932*a(n-14) -14992866*a(n-15) -49988407*a(n-16) +16438786*a(n-17) +31549556*a(n-18) -9212528*a(n-19) -13108544*a(n-20) +2853616*a(n-21) +3512372*a(n-22) -487178*a(n-23) -584214*a(n-24) +44610*a(n-25) +58000*a(n-26) -2006*a(n-27) -3248*a(n-28) +34*a(n-29) +92*a(n-30) -a(n-32)

%e Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)

%e ..0..0..0....6..4..0....6..4..7....0..0..0....0..6..4....6..4..0....0..0..7

%e ..0..0..0....0..0..0....0..3..0....0..6..4....6..4..7....6..4..0....0..3..0

%e ..0..0..7....6..4..0....0..0..0....0..0..0....0..3..0....0..0..0....0..0..7

%e ..0..3..0....6..4..0....6..4..7....6..4..0....0..0..0....0..7..0....0..3..0

%e ..0..0..0....6..4..0....0..3..0....6..4..0....0..0..0....3..0..0....0..6..4

%K nonn

%O 1,2

%A _R. H. Hardin_ Dec 16 2012