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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. _ _ _ _ |_|_|_|_|_ |_|_|_|_| (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 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

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