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A220684 Number of ways to reciprocally link elements of an nX4 array either to themselves or to exactly two horizontal, vertical or antidiagonal neighbors.

%I A220684 #6 Jul 23 2025 01:21:40
%S A220684 1,37,745,15452,312603,6349886,128995678,2620320833,53226950200,
%T A220684 1081210102382,21962842195925,446135673339403,9062444632025696,
%U A220684 184087280486642815,3739402357364779367,75959240384539034764
%N A220684 Number of ways to reciprocally link elements of an nX4 array either to themselves or to exactly two horizontal, vertical or antidiagonal neighbors.
%C A220684 Column 4 of A220688
%H A220684 R. H. Hardin, <a href="/A220684/b220684.txt">Table of n, a(n) for n = 1..210</a>
%F A220684 Empirical: a(n) = 15*a(n-1) +89*a(n-2) +365*a(n-3) +522*a(n-4) -1997*a(n-5) -10213*a(n-6) -23837*a(n-7) -26018*a(n-8) +7514*a(n-9) +19116*a(n-10) -3306*a(n-11) -5327*a(n-12) +2212*a(n-13) +316*a(n-14) -285*a(n-15) +12*a(n-17) -a(n-18)
%e A220684 Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
%e A220684 .00.67.48.78...68.46.46.47...00.00.00.78...00.00.68.48...68.46.46.47
%e A220684 .38.78.23.27...26.48.37.00...00.67.34.27...00.68.24.27...28.00.38.00
%e A220684 .23.26.34.00...00.23.00.00...36.46.34.00...00.26.34.00...26.46.24.00
%K A220684 nonn
%O A220684 1,2
%A A220684 _R. H. Hardin_ Dec 17 2012