cp's OEIS Frontend

A220634 Number of ways to reciprocally link elements of an 4 X n array either to themselves or to exactly two horizontal or antidiagonal neighbors.

%I A220634 #7 Aug 02 2018 04:59:22
%S A220634 1,1,5,37,257,1665,10695,68637,440509,2827377,18148003,116487861,
%T A220634 747713321,4799439985,30806785967,197743565181,1269282762917,
%U A220634 8147313444929,52296241209451,335680820572405,2154679016567857
%N A220634 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 A220634 Row 4 of A220632.
%H A220634 R. H. Hardin, <a href="/A220634/b220634.txt">Table of n, a(n) for n = 1..210</a>
%F A220634 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 A220634 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 A220634 All solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):
%e A220634 .00.00.00...00.00.00...00.67.47...00.67.47...00.00.00
%e A220634 .00.00.00...00.00.00...36.34.00...36.34.00...00.67.47
%e A220634 .00.67.47...00.00.00...00.67.47...00.00.00...36.34.00
%e A220634 .36.34.00...00.00.00...36.34.00...00.00.00...00.00.00
%Y A220634 Cf. A220632.
%K A220634 nonn
%O A220634 1,3
%A A220634 _R. H. Hardin_, Dec 17 2012