cp's OEIS Frontend

A220563 Number of ways to reciprocally link elements of an 2 X n array either to themselves or to exactly one horizontal or antidiagonal neighbor.

%I A220563 #23 Nov 01 2024 23:39:20
%S A220563 1,5,14,47,149,481,1544,4965,15957,51293,164870,529947,1703417,
%T A220563 5475329,17599456,56570281,181834969,584475733,1878691886,6038716423,
%U A220563 19410365421,62391120801,200545011400,644615789581,2072001259341,6660074556205
%N A220563 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 A220563 Row 2 of A220562.
%C A220563 From _Wajdi Maaloul_, Jul 04 2022: (Start)
%C A220563 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.
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%C A220563 (End)
%H A220563 R. H. Hardin, <a href="/A220563/b220563.txt">Table of n, a(n) for n = 1..210</a>
%H A220563 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,0,-1).
%F A220563 a(n) = 2*a(n-1) + 4*a(n-2) - a(n-4).
%F A220563 G.f.: x*(1 + 3*x - x^3) / ((1 + x)*(1 - 3*x - x^2 + x^3)). - _Colin Barker_, Jul 31 2018
%F A220563 For n>0, a(n) = A316726(n+1) - A033505(n+1). - _Wajdi Maaloul_, Jul 04 2022
%e A220563 Some solutions for n=3, 0=self, 3=ne, 4=w, 6=e, 7=sw (reciprocal directions total 10):
%e A220563   0 6 4   0 0 0   0 7 0   6 4 0   0 0 0   0 7 0   0 6 4
%e A220563   0 6 4   0 0 0   3 6 4   0 0 0   0 6 4   3 0 0   0 0 0
%Y A220563 Cf. A220562.
%K A220563 nonn,easy
%O A220563 1,2
%A A220563 _R. H. Hardin_, Dec 16 2012