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.

1, 5, 14, 47, 149, 481, 1544, 4965, 15957, 51293, 164870, 529947, 1703417, 5475329, 17599456, 56570281, 181834969, 584475733, 1878691886, 6038716423, 19410365421, 62391120801, 200545011400, 644615789581, 2072001259341, 6660074556205

Offset: 1

Author

R. H. Hardin, Dec 16 2012

Keywords

• nonn
• easy

Comments

Row 2 of A220562.

From Wajdi Maaloul, Jul 04 2022: (Start)

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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(End)

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Index entries for linear recurrences with constant coefficients, signature (2,4,0,-1).

Crossrefs

Cf. A220562.

Formula

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

G.f.: x*(1 + 3*x - x^3) / ((1 + x)*(1 - 3*x - x^2 + x^3)). - Colin Barker, Jul 31 2018

For n>0, a(n) = A316726(n+1) - A033505(n+1). - Wajdi Maaloul, Jul 04 2022