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A220619 Number of ways to reciprocally link elements of an nX6 array either to themselves or to exactly one horizontal, diagonal and antidiagonal neighbor.

%I A220619 #6 Jul 23 2025 01:18:13
%S A220619 13,1215,76955,5280827,356768525,24177895648,1637496710797,
%T A220619 110916199227139,7512747980759983,508867505795261823,
%U A220619 34467532553765146717,2334617570886588879553,158132555108084876751600
%N A220619 Number of ways to reciprocally link elements of an nX6 array either to themselves or to exactly one horizontal, diagonal and antidiagonal neighbor.
%C A220619 Column 6 of A220621
%H A220619 R. H. Hardin, <a href="/A220619/b220619.txt">Table of n, a(n) for n = 1..210</a>
%F A220619 Empirical: a(n) = 75*a(n-1) -234*a(n-2) -18880*a(n-3) +81906*a(n-4) +899610*a(n-5) -3495200*a(n-6) -14871391*a(n-7) +57262153*a(n-8) +94978240*a(n-9) -425367914*a(n-10) -207014564*a(n-11) +1449829450*a(n-12) +111910344*a(n-13) -2364082704*a(n-14) -29030256*a(n-15) +1700883948*a(n-16) +349734858*a(n-17) -215936884*a(n-18) -545425394*a(n-19) -380424104*a(n-20) +341201464*a(n-21) +219237544*a(n-22) -120388312*a(n-23) -52194454*a(n-24) +28101292*a(n-25) +7351846*a(n-26) -4063344*a(n-27) -843527*a(n-28) +300917*a(n-29) +79254*a(n-30) -10858*a(n-31) -4326*a(n-32) +168*a(n-33) +112*a(n-34) -a(n-35) -a(n-36)
%e A220619 Some solutions for n=3 0=self 1=nw 3=ne 4=w 6=e 7=sw 9=se (reciprocal directions total 10)
%e A220619 ..6..4..0..6..4..0....0..7..9..7..0..0....9..9..9..0..6..4....6..4..9..0..9..0
%e A220619 ..0..9..7..9..9..0....3..7..3..1..6..4....0..1..1..1..7..0....9..9..0..1..7..1
%e A220619 ..0..3..1..0..1..1....3..0..0..6..4..0....0..6..4..3..6..4....0..1..1..3..0..0
%K A220619 nonn
%O A220619 1,1
%A A220619 _R. H. Hardin_ Dec 17 2012