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A220712 Number of ways to reciprocally link elements of an 7Xn array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.

%I A220712 #6 Jul 23 2025 01:22:39
%S A220712 1,1,21,129,932,6412,44976,311193,2168111,15034974,104478616,
%T A220712 725286308,5037269200,34977393156,242898931716,1686719471828,
%U A220712 11713075485508,81338093590180,564832581201972,3922330554994484,27237632538545092
%N A220712 Number of ways to reciprocally link elements of an 7Xn array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.
%C A220712 Row 7 of A220708
%H A220712 R. H. Hardin, <a href="/A220712/b220712.txt">Table of n, a(n) for n = 1..210</a>
%F A220712 Empirical: a(n) = a(n-1) +76*a(n-2) -4*a(n-3) -2156*a(n-4) -520*a(n-5) +32432*a(n-6) +9800*a(n-7) -296352*a(n-8) -80128*a(n-9) +1755472*a(n-10) +365536*a(n-11) -6970672*a(n-12) -1003248*a(n-13) +18839680*a(n-14) +1679040*a(n-15) -34716928*a(n-16) -1650048*a(n-17) +43135744*a(n-18) +820736*a(n-19) -35163136*a(n-20) -61440*a(n-21) +17813504*a(n-22) -116736*a(n-23) -5017600*a(n-24) +36864*a(n-25) +589824*a(n-26) for n>32
%e A220712 Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)
%e A220712 .00.67.47...00.00.00...00.00.00...00.67.47...00.67.47...00.67.47...00.00.00
%e A220712 .36.34.00...00.00.00...00.67.47...36.34.00...36.34.00...36.34.00...00.00.00
%e A220712 .00.00.00...00.67.47...36.34.00...00.67.47...00.67.47...00.67.47...00.67.47
%e A220712 .00.00.00...36.34.00...00.00.00...36.34.00...36.34.00...36.34.00...36.34.00
%e A220712 .00.00.00...00.00.00...00.67.47...00.00.00...00.00.00...00.67.47...00.00.00
%e A220712 .00.00.00...00.00.00...36.34.00...00.67.47...00.00.00...36.34.00...00.67.47
%e A220712 .00.00.00...00.00.00...00.00.00...36.34.00...00.00.00...00.00.00...36.34.00
%K A220712 nonn
%O A220712 1,3
%A A220712 _R. H. Hardin_ Dec 18 2012