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A220739
Number of ways to reciprocally link elements of an 2 X n array either to themselves or to exactly two horizontal, diagonal and antidiagonal neighbors, without consecutive collinear links.
1
1, 2, 5, 13, 32, 85, 221, 578, 1513, 3961, 10368, 27145, 71065, 186050, 487085, 1275205, 3338528, 8740381, 22882613, 59907458, 156839761, 410611825, 1074995712, 2814375313, 7368130225, 19290015362, 50501915861, 132215732221
OFFSET
1,2
COMMENTS
Row 2 of A220738.
LINKS
FORMULA
Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 2*a(n-4) - 2*a(n-5) + a(n-6).
Empirical g.f.: x*(1 - x^2 - x^3 - 2*x^4 + x^5) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)*(1 + x + x^2)). - Colin Barker, Aug 03 2018
EXAMPLE
All solutions for n=3 0=self 1=nw 3=ne 4=w 6=e 7=sw 9=se (reciprocal directions total 10):
.69.47.00...00.69.47...00.67.47...69.49.00...00.00.00
.36.14.00...00.36.14...36.34.00...00.16.14...00.00.00
CROSSREFS
Cf. A220738.
Sequence in context: A110320 A219230 A108890 * A337282 A366117 A027929
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 18 2012
STATUS
approved