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A220567 Number of ways to reciprocally link elements of an 6Xn array either to themselves or to exactly one horizontal or antidiagonal neighbor.

%I A220567 #6 Jul 23 2025 01:13:58
%S A220567 1,233,6076,338581,14298089,665748170,29955561052,1363847439227,
%T A220567 61845935792336,2808292682072854,127461441592952329,
%U A220567 5786012622635830257,262638882187378528534,11921898805633926722093,541164958214032363841199
%N A220567 Number of ways to reciprocally link elements of an 6Xn array either to themselves or to exactly one horizontal or antidiagonal neighbor.
%C A220567 Row 6 of A220562
%H A220567 R. H. Hardin, <a href="/A220567/b220567.txt">Table of n, a(n) for n = 1..210</a>
%F A220567 Empirical: a(n) = 13*a(n-1) +1348*a(n-2) +10654*a(n-3) -198504*a(n-4) -1906076*a(n-5) +16144268*a(n-6) +135853346*a(n-7) -925177576*a(n-8) -4891188529*a(n-9) +35999318281*a(n-10) +81980396412*a(n-11) -848296316904*a(n-12) -276758340388*a(n-13) +11227641980488*a(n-14) -7107958733596*a(n-15) -92787258095632*a(n-16) +107881224287236*a(n-17) +525583351897147*a(n-18) -774675289613655*a(n-19) -2182902615756840*a(n-20) +3555500220788694*a(n-21) +6973910104740084*a(n-22) -11426713159097796*a(n-23) -17667940720548336*a(n-24) +26747813225197794*a(n-25) +35945989169311476*a(n-26) -46394604844529149*a(n-27) -58560503957694547*a(n-28) +59946651607436776*a(n-29) +75473026016657552*a(n-30) -57619701988418728*a(n-31) -75893814357642448*a(n-32) +40983675195728936*a(n-33) +58931290214948032*a(n-34) -21385512054198856*a(n-35) -35152757210761395*a(n-36) +8057875480743783*a(n-37) +16091164614749124*a(n-38) -2117225467318182*a(n-39) -5658108579422624*a(n-40) +352030436802844*a(n-41) +1530178310024236*a(n-42) -22441127837162*a(n-43) -318296736753680*a(n-44) -5136539584403*a(n-45) +50823610079499*a(n-46) +1734560714908*a(n-47) -6199297816488*a(n-48) -263242733620*a(n-49) +572842763656*a(n-50) +25065179764*a(n-51) -39590221744*a(n-52) -1591760572*a(n-53) +2008410297*a(n-54) +67587747*a(n-55) -72760800*a(n-56) -1863630*a(n-57) +1806100*a(n-58) +31300*a(n-59) -28744*a(n-60) -282*a(n-61) +260*a(n-62) +a(n-63) -a(n-64)
%e A220567 Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)
%e A220567 ..0..7..7....0..0..0....6..4..7....0..7..0....0..7..0....0..0..0....0..6..4
%e A220567 ..3..3..0....6..4..0....0..3..0....3..6..4....3..7..0....6..4..0....6..4..7
%e A220567 ..6..4..0....0..6..4....0..6..4....6..4..0....3..0..0....0..0..0....0..3..0
%e A220567 ..0..0..0....6..4..7....6..4..0....0..7..0....0..7..0....0..0..0....0..0..7
%e A220567 ..0..7..0....0..3..0....0..6..4....3..7..0....3..7..7....0..0..7....0..3..0
%e A220567 ..3..0..0....0..6..4....0..6..4....3..6..4....3..3..0....0..3..0....6..4..0
%K A220567 nonn
%O A220567 1,2
%A A220567 _R. H. Hardin_ Dec 16 2012