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

1,2

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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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

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

Crossrefs

Cf. A220562.

Sequence in context: A163608 A081496 A152051 * A075827 A134418 A272147

Adjacent sequences: A220560 A220561 A220562 * A220564 A220565 A220566

Keyword

nonn,easy

Author

R. H. Hardin, Dec 16 2012

Status

approved