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A220550 Number of ways to reciprocally link elements of an nX5 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.

%I A220550 #6 Jul 23 2025 01:12:47
%S A220550 8,401,14556,565061,21668208,832899775,32001129185,1229633337183,
%T A220550 47247493674864,1815445803499208,69756959373004005,
%U A220550 2680352078247056300,102990256079543046348,3957313286001327139326,152056408321267850998276
%N A220550 Number of ways to reciprocally link elements of an nX5 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.
%C A220550 Column 5 of A220553
%H A220550 R. H. Hardin, <a href="/A220550/b220550.txt">Table of n, a(n) for n = 1..210</a>
%F A220550 Empirical: a(n) = 21*a(n-1) +607*a(n-2) +2818*a(n-3) -13422*a(n-4) -102307*a(n-5) +102787*a(n-6) +1377367*a(n-7) -625026*a(n-8) -9368158*a(n-9) +6655110*a(n-10) +30101928*a(n-11) -31218870*a(n-12) -45617582*a(n-13) +65294634*a(n-14) +29766481*a(n-15) -68435485*a(n-16) -4100689*a(n-17) +40652394*a(n-18) -5180290*a(n-19) -14692966*a(n-20) +3231432*a(n-21) +3351718*a(n-22) -849954*a(n-23) -490034*a(n-24) +118041*a(n-25) +45619*a(n-26) -8829*a(n-27) -2574*a(n-28) +334*a(n-29) +79*a(n-30) -5*a(n-31) -a(n-32)
%e A220550 Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
%e A220550 ..0..7..0..0..7....0..6..4..8..8....8..6..4..0..0....8..0..8..0..7
%e A220550 ..3..6..4..3..7....0..0..8..2..2....2..7..8..0..7....2..0..2..3..0
%e A220550 ..6..4..0..3..0....6..4..2..6..4....3..0..2..3..0....0..0..0..6..4
%K A220550 nonn
%O A220550 1,1
%A A220550 _R. H. Hardin_ Dec 15 2012