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A220598 Number of ways to reciprocally link elements of an nX4 array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops.

%I A220598 #6 Jul 23 2025 01:16:57
%S A220598 1,17,471,9047,167614,3174778,60138423,1137615308,21523535122,
%T A220598 407249783145,7705461280893,145792738613760,2758505816300670,
%U A220598 52192947928719778,987528662199324496,18684763495713245969
%N A220598 Number of ways to reciprocally link elements of an nX4 array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without 3-loops.
%C A220598 Column 4 of A220602
%H A220598 R. H. Hardin, <a href="/A220598/b220598.txt">Table of n, a(n) for n = 1..210</a>
%F A220598 Empirical: a(n) = 15*a(n-1) +41*a(n-2) +606*a(n-3) +405*a(n-4) +679*a(n-5) -8407*a(n-6) -28555*a(n-7) +17039*a(n-8) +147483*a(n-9) +79534*a(n-10) -260454*a(n-11) -334003*a(n-12) +79493*a(n-13) +384190*a(n-14) +187418*a(n-15) -93878*a(n-16) -122508*a(n-17) -48185*a(n-18) -5142*a(n-19) +3204*a(n-20) +1023*a(n-21) +22*a(n-22) -9*a(n-23) -11*a(n-24) +a(n-25)
%e A220598 Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
%e A220598 .00.68.46.48...68.48.67.47...00.67.46.48...68.48.00.78...00.68.48.78
%e A220598 .00.27.00.28...28.23.36.48...38.67.47.28...26.24.37.28...00.27.23.28
%e A220598 .36.46.46.24...26.46.46.24...23.36.46.24...00.36.46.24...36.46.46.24
%K A220598 nonn
%O A220598 1,2
%A A220598 _R. H. Hardin_ Dec 16 2012