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A220625 Number of ways to reciprocally link elements of an 6Xn array either to themselves or to exactly one horizontal, diagonal and antidiagonal neighbor.

%I A220625 #6 Jul 23 2025 01:18:55
%S A220625 1,733,28373,3466455,262680517,24177895648,2054706174413,
%T A220625 180411767818111,15630369162961753,1361611598697855401,
%U A220625 118348460320274885509,10296062072472866977053,895398179175506044479552
%N A220625 Number of ways to reciprocally link elements of an 6Xn array either to themselves or to exactly one horizontal, diagonal and antidiagonal neighbor.
%C A220625 Row 6 of A220621
%H A220625 R. H. Hardin, <a href="/A220625/b220625.txt">Table of n, a(n) for n = 1..210</a>
%F A220625 Empirical: a(n) = 63*a(n-1) +2862*a(n-2) -60440*a(n-3) -824202*a(n-4) +18146150*a(n-5) -20045386*a(n-6) -921241585*a(n-7) +3855313257*a(n-8) +9737277088*a(n-9) -97429928112*a(n-10) +108733427540*a(n-11) +757492139660*a(n-12) -1932297359512*a(n-13) -1293178837092*a(n-14) +7244830922052*a(n-15) -3341781023928*a(n-16) -7386155450412*a(n-17) +15850519492508*a(n-18) -14572332601872*a(n-19) -15900073555920*a(n-20) +32949026690632*a(n-21) -1615780730832*a(n-22) -14531450950368*a(n-23) +3100647563872*a(n-24) +425129425324*a(n-25) -23935477836*a(n-26) +300359574120*a(n-27) +63008127325*a(n-28) +37808128429*a(n-29) -35095894230*a(n-30) -6841941084*a(n-31) -750501810*a(n-32) +796187034*a(n-33) -8202438*a(n-34) -1789695*a(n-35) -552825*a(n-36)
%e A220625 Some solutions for n=3 0=self 1=nw 3=ne 4=w 6=e 7=sw 9=se (reciprocal directions total 10)
%e A220625 ..0..6..4....6..4..0....0..6..4....0..0..0....0..9..0....0..0..0....9..6..4
%e A220625 ..0..0..0....6..4..0....9..9..0....0..9..0....9..7..1....0..0..0....0..1..7
%e A220625 ..0..7..0....0..0..0....0..1..1....0..7..1....3..1..7....6..4..0....0..3..0
%e A220625 ..3..7..0....9..7..0....6..4..7....3..0..0....0..3..0....6..4..7....0..6..4
%e A220625 ..3..0..0....3..1..0....0..3..0....9..7..0....0..7..0....0..3..0....0..6..4
%e A220625 ..6..4..0....0..6..4....0..6..4....3..1..0....3..0..0....0..0..0....0..6..4
%K A220625 nonn
%O A220625 1,2
%A A220625 _R. H. Hardin_ Dec 17 2012