A220558 - OEIS

%I #7 Jul 31 2018 14:31:37

%S 5,47,430,3966,36640,338581,3128843,28913910,267196106,2469184016,

%T 22817958901,210862878471,1948603453870,18007225586854,

%U 166406444930000,1537777420552101,14210744037917219,131322806156626838

%N Number of ways to reciprocally link elements of an n X 4 array either to themselves or to exactly one horizontal or antidiagonal neighbor.

%C Column 4 of A220562.

%H R. H. Hardin, <a href="/A220558/b220558.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 11*a(n-1) - 17*a(n-2) + 7*a(n-3) - a(n-4).

%F Empirical g.f.: x*(5 - 8*x - 2*x^2) / (1 - 11*x + 17*x^2 - 7*x^3 + x^4). - _Colin Barker_, Jul 31 2018

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

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

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

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

%Y Cf. A220562.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 16 2012