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A220623 Number of ways to reciprocally link elements of an 4Xn array either to themselves or to exactly one horizontal, diagonal and antidiagonal neighbor.

%I A220623 #6 Jul 23 2025 01:18:41
%S A220623 1,71,765,17084,282777,5280827,93905509,1703300073,30648000256,
%T A220623 553256525421,9974206108397,179912817659011,3244530759637569,
%U A220623 58516690759430228,1055339507419304093,19033159346284815815
%N A220623 Number of ways to reciprocally link elements of an 4Xn array either to themselves or to exactly one horizontal, diagonal and antidiagonal neighbor.
%C A220623 Row 4 of A220621
%H A220623 R. H. Hardin, <a href="/A220623/b220623.txt">Table of n, a(n) for n = 1..210</a>
%F A220623 Empirical: a(n) = 14*a(n-1) +98*a(n-2) -452*a(n-3) -102*a(n-4) +876*a(n-5) -144*a(n-6) -268*a(n-7) +22*a(n-8) -8*a(n-9) +15*a(n-10)
%e A220623 Some solutions for n=3 0=self 1=nw 3=ne 4=w 6=e 7=sw 9=se (reciprocal directions total 10)
%e A220623 ..0..6..4....6..4..0....6..4..0....0..6..4....0..7..0....0..0..7....9..9..0
%e A220623 ..0..6..4....6..4..0....0..9..0....0..9..0....3..9..0....0..3..0....0..1..1
%e A220623 ..0..7..7....0..0..0....9..0..1....0..0..1....0..0..1....9..7..0....6..4..0
%e A220623 ..3..3..0....0..6..4....0..1..0....0..0..0....6..4..0....3..1..0....6..4..0
%K A220623 nonn
%O A220623 1,2
%A A220623 _R. H. Hardin_ Dec 17 2012