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A220551 Number of ways to reciprocally link elements of an nX6 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.

%I A220551 #6 Jul 23 2025 01:12:55
%S A220551 13,1490,117022,9943416,832899775,69961268156,5873481159019,
%T A220551 493147308003276,41404696495593733,3476354713685117295,
%U A220551 291875923358702188677,24506004816897100837250,2057532704150988606181644
%N A220551 Number of ways to reciprocally link elements of an nX6 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.
%C A220551 Column 6 of A220553
%H A220551 R. H. Hardin, <a href="/A220551/b220551.txt">Table of n, a(n) for n = 1..210</a>
%F A220551 Empirical: a(n) = 43*a(n-1) +3071*a(n-2) +35931*a(n-3) -339473*a(n-4) -7161173*a(n-5) +10510607*a(n-6) +579287390*a(n-7) -86009834*a(n-8) -26973137653*a(n-9) +17922247043*a(n-10) +759668332883*a(n-11) -1458641637557*a(n-12) -10811736525989*a(n-13) +34648043396638*a(n-14) +69138971017482*a(n-15) -378744880646789*a(n-16) -76869384351785*a(n-17) +2257136247846663*a(n-18) -1481921417023445*a(n-19) -8203392366781665*a(n-20) +10251619124403834*a(n-21) +19428261339797202*a(n-22) -35703350984991269*a(n-23) -30990769502166197*a(n-24) +81734131713586135*a(n-25) +33362269139093511*a(n-26) -134985540835357813*a(n-27) -23195971096184462*a(n-28) +168796132411857454*a(n-29) +8920475172874387*a(n-30) -164274545229295041*a(n-31) -1102569342380921*a(n-32) +126129771048509667*a(n-33) +1130153727733123*a(n-34) -76604004519697618*a(n-35) -3244753679232374*a(n-36) +36583369819597543*a(n-37) +3421670217601687*a(n-38) -13573387285852645*a(n-39) -2076638760328461*a(n-40) +3850117905476135*a(n-41) +830228772519594*a(n-42) -818857176583502*a(n-43) -229995045268009*a(n-44) +127535909598535*a(n-45) +45050732663975*a(n-46) -14097155555237*a(n-47) -6284132716629*a(n-48) +1051348389402*a(n-49) +624786901206*a(n-50) -47058515857*a(n-51) -44115713573*a(n-52) +699849703*a(n-53) +2192996827*a(n-54) +48467383*a(n-55) -75562626*a(n-56) -3337706*a(n-57) +1759671*a(n-58) +92567*a(n-59) -26561*a(n-60) -1265*a(n-61) +239*a(n-62) +7*a(n-63) -a(n-64)
%e A220551 Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
%e A220551 ..6..4..7..0..8..0....0..0..0..6..4..8....0..8..0..0..0..7....8..0..0..0..8..8
%e A220551 ..8..3..6..4..2..7....6..4..0..6..4..2....0..2..0..8..3..0....2..0..0..8..2..2
%e A220551 ..2..6..4..0..3..0....0..0..0..0..0..0....6..4..0..2..0..0....0..6..4..2..0..0
%K A220551 nonn
%O A220551 1,1
%A A220551 _R. H. Hardin_ Dec 15 2012