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A220565 Number of ways to reciprocally link elements of an 4Xn array either to themselves or to exactly one horizontal or antidiagonal neighbor.

%I A220565 #6 Jul 23 2025 01:13:43
%S A220565 1,34,292,3966,45966,561636,6743873,81437539,981628768,11839220919,
%T A220565 142763980945,1721628751022,20761198193082,250361650578082,
%U A220565 3019134246246588,36408038586112352,439048064386701057
%N A220565 Number of ways to reciprocally link elements of an 4Xn array either to themselves or to exactly one horizontal or antidiagonal neighbor.
%C A220565 Row 4 of A220562
%H A220565 R. H. Hardin, <a href="/A220565/b220565.txt">Table of n, a(n) for n = 1..210</a>
%F A220565 Empirical: a(n) = 4*a(n-1) +84*a(n-2) +194*a(n-3) -338*a(n-4) -1077*a(n-5) +616*a(n-6) +1932*a(n-7) -788*a(n-8) -1136*a(n-9) +325*a(n-10) +284*a(n-11) -48*a(n-12) -30*a(n-13) +2*a(n-14) +a(n-15)
%e A220565 Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)
%e A220565 ..0..6..4....0..6..4....0..6..4....0..7..0....0..0..0....6..4..0....6..4..0
%e A220565 ..0..0..0....0..7..0....0..7..0....3..0..0....6..4..0....0..6..4....0..7..0
%e A220565 ..0..7..0....3..6..4....3..6..4....6..4..7....0..6..4....0..7..7....3..0..0
%e A220565 ..3..0..0....0..6..4....0..0..0....0..3..0....0..6..4....3..3..0....0..0..0
%K A220565 nonn
%O A220565 1,2
%A A220565 _R. H. Hardin_ Dec 16 2012