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A220676 Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without consecutive collinear links. 1
1, 9, 43, 201, 968, 4604, 22000, 104976, 501096, 2391737, 11415981, 54489429, 260082487, 1241395361, 5925282424, 28281863304, 134991671188, 644326407852, 3075423213984, 14679249263905, 70065270353385, 334427328092001 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 3 of A220681.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 2*a(n-1) + 11*a(n-2) + 10*a(n-3) + 2*a(n-4) + 5*a(n-5) + 4*a(n-6) - a(n-7).

Empirical g.f.: x*(1 + 7*x + 14*x^2 + 6*x^3 + x^4 + 4*x^5 - x^6) / ((1 + x)*(1 - 3*x - 8*x^2 - 2*x^3 - 5*x^5 + x^6)). - Colin Barker, Aug 02 2018

EXAMPLE

Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10):

.00.00.00...00.67.48...68.47.00...68.47.00...00.78.00...68.48.00...00.00.00

.00.68.47...38.68.24...23.78.00...23.68.47...38.27.78...26.24.00...68.48.00

.00.23.00...26.24.00...36.24.00...00.23.00...23.36.24...00.00.00...26.24.00

CROSSREFS

Cf. A220681.

Sequence in context: A259181 A330088 A281773 * A110125 A221751 A275793

Adjacent sequences: A220673 A220674 A220675 * A220677 A220678 A220679

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 17 2012

STATUS

approved

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Last modified November 27 11:32 EST 2022. Contains 358403 sequences. (Running on oeis4.)