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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
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Dec 16 2012
STATUS
approved

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Last modified February 26 11:46 EST 2024. Contains 370352 sequences. (Running on oeis4.)