A220563 - OEIS

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

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OFFSET

1,2

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)

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).

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

EXAMPLE