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A220622 Number of ways to reciprocally link elements of an 3 X n array either to themselves or to exactly one horizontal, diagonal and antidiagonal neighbor 1

%I

%S 1,22,125,1189,9176,76955,624227,5131406,41957895,343809419,

%T 2814822600,23053276257,188779537161,1545969533334,12660108907789,

%U 103675885828389,849017313171328,6952739324271787,56937068599653211,466266655043137726

%N Number of ways to reciprocally link elements of an 3 X n array either to themselves or to exactly one horizontal, diagonal and antidiagonal neighbor

%C Row 3 of A220621.

%H R. H. Hardin, <a href="/A220622/b220622.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) + 22*a(n-2) - 32*a(n-3) - 12*a(n-4) + 8*a(n-5) - 3*a(n-6).

%F Empirical g.f.: x*(1 + 16*x - 29*x^2 - 13*x^3 + 8*x^4 - 3*x^5) / (1 - 6*x - 22*x^2 + 32*x^3 + 12*x^4 - 8*x^5 + 3*x^6). - _Colin Barker_, Aug 01 2018

%e Some solutions for n=3 0=self 1=nw 3=ne 4=w 6=e 7=sw 9=se (reciprocal directions total 10):

%e ..6..4..0....0..6..4....0..7..0....0..0..0....6..4..0....0..7..0....0..7..0

%e ..0..0..0....0..6..4....3..6..4....0..0..0....9..9..0....3..6..4....3..0..7

%e ..0..0..0....6..4..0....0..6..4....0..6..4....0..1..1....0..0..0....0..3..0

%Y Cf. A220621.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 17 2012

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Last modified August 15 17:39 EDT 2022. Contains 356148 sequences. (Running on oeis4.)