%I #20 Aug 24 2022 10:02:45

%S 1,5,14,47,149,481,1544,4965,15957,51293,164870,529947,1703417,

%T 5475329,17599456,56570281,181834969,584475733,1878691886,6038716423,

%U 19410365421,62391120801,200545011400,644615789581,2072001259341,6660074556205

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

%C Row 2 of A220562.

%C From _Wajdi Maaloul_, Jul 04 2022: (Start)

%C For n > 0, a(n) is the number of ways to tile the S-shaped figure of length n below with squares and dominoes. For instance, a(4) is the number of ways to tile this figure with squares and dominoes.

%C _ _ _ _

%C |_|_|_|_|_

%C |_|_|_|_|

%C (End)

%H R. H. Hardin, <a href="/A220563/b220563.txt">Table of n, a(n) for n = 1..210</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,0,-1).

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

%F G.f.: x*(1 + 3*x - x^3) / ((1 + x)*(1 - 3*x - x^2 + x^3). - _Colin Barker_, Jul 31 2018

%F For n>0, a(n) = A316726(n+1) - A033505(n+1). - _Wajdi Maaloul_, Jul 04 2022

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

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

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

%Y Cf. A220562.

%K nonn,easy

%O 1,2

%A _R. H. Hardin_, Dec 16 2012