A220547 - OEIS

%I #12 Jan 10 2021 22:20:09

%S 2,8,29,108,401,1490,5536,20569,76424,283953,1055026,3919944,14564533,

%T 54114452,201061985,747044834,2775641472,10312882481,38317465040,

%U 142368356257,528968939938,1965381541064,7302365621709,27131904192124

%N Number of ways to reciprocally link elements of an n X 2 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.

%C Column 2 of A220553.

%H R. H. Hardin, <a href="/A220547/b220547.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(1 + x)*(2 - x^2) / (1 - 3*x - 3*x^2 + x^3 + x^4). - _Colin Barker_, Mar 13 2018

%F Empirical: a(n) = A000078(2*n + 3). - _Greg Dresden_, Jan 10 2021

%e Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10):

%e ..8..8....0..7....6..4....6..4....8..0....0..0....0..0....0..0....0..8....6..4

%e ..2..2....3..8....0..0....6..4....2..8....8..8....0..8....0..0....8..2....8..8

%e ..6..4....0..2....0..0....0..0....0..2....2..2....0..2....0..0....2..0....2..2

%Y Cf. A220553, A000078.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 15 2012