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Number of ways to reciprocally link elements of an 4 X n array either to themselves or to exactly two horizontal or antidiagonal neighbors.
1

%I #7 Aug 02 2018 04:59:22

%S 1,1,5,37,257,1665,10695,68637,440509,2827377,18148003,116487861,

%T 747713321,4799439985,30806785967,197743565181,1269282762917,

%U 8147313444929,52296241209451,335680820572405,2154679016567857

%N Number of ways to reciprocally link elements of an 4 X n array either to themselves or to exactly two horizontal or antidiagonal neighbors.

%C Row 4 of A220632.

%H R. H. Hardin, <a href="/A220634/b220634.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*a(n-1) - 16*a(n-2) - 6*a(n-3) + 15*a(n-4) + a(n-5) - 2*a(n-6) for n>9.

%F Empirical g.f.: x*(1 - 8*x + 12*x^2 + 14*x^3 - 5*x^4 - 42*x^5 - 30*x^6 + 6*x^7 + 4*x^8) / ((1 - x)*(1 - 2*x - x^2)*(1 - 6*x - 3*x^2 + 2*x^3)). - _Colin Barker_, Aug 02 2018

%e All solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):

%e .00.00.00...00.00.00...00.67.47...00.67.47...00.00.00

%e .00.00.00...00.00.00...36.34.00...36.34.00...00.67.47

%e .00.67.47...00.00.00...00.67.47...00.00.00...36.34.00

%e .36.34.00...00.00.00...36.34.00...00.00.00...00.00.00

%Y Cf. A220632.

%K nonn

%O 1,3

%A _R. H. Hardin_, Dec 17 2012