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A185818 1/5 the number of n X 2 0..4 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

%I A185818 #19 Jul 23 2018 21:06:48
%S A185818 1,9,76,656,5680,49248,426928,3701360,32089696,278208816,2411993584,
%T A185818 20911320416,181295389360,1571781109104,13626909445216,
%U A185818 118141552910384,1024254735084784,8880006538838880,76987211704914352,667457928119357552
%N A185818 1/5 the number of n X 2 0..4 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.
%C A185818 Column 2 of A185825.
%H A185818 R. H. Hardin, <a href="/A185818/b185818.txt">Table of n, a(n) for n = 1..200</a>
%H A185818 Robert Israel, <a href="/A185818/a185818.pdf">Maple-assisted proof of formula</a>
%F A185818 Empirical: a(n) = 7*a(n-1) + 15*a(n-2) - 32*a(n-4) - 64*a(n-5).
%F A185818 Empirical g.f.: x*(1 + 2*x - 2*x^2 - 11*x^3 - 20*x^4) / (1 - 7*x - 15*x^2 + 32*x^4 + 64*x^5). - _Colin Barker_, Apr 16 2018
%F A185818 Empirical formulas verified (see link). - _Robert Israel_, Jul 23 2018
%e A185818 Some solutions for 4 X 2 with a(1,1)=0:
%e A185818 ..0..2....0..0....0..0....0..0....0..0....0..0....0..3....0..0....0..0....0..0
%e A185818 ..0..2....1..1....0..0....0..3....3..2....2..0....0..3....3..4....0..2....0..3
%e A185818 ..1..1....1..1....4..4....4..3....3..2....2..0....2..3....3..4....4..2....3..3
%e A185818 ..0..0....0..0....3..3....4..3....3..3....1..1....2..2....3..4....4..2....2..2
%p A185818 f:= gfun:-rectoproc({a(n) = 7*a(n-1) + 15*a(n-2) - 32*a(n-4) - 64*a(n-5), a(1)=1, a(2)=9, a(3)=76, a(4)=656, a(5)=5680},a(n),remember):
%p A185818 map(f, [$1..30]); # _Robert Israel_, Jul 23 2018
%o A185818 (PARI) x='x+O('x^99); Vec(x*(1+2*x-2*x^2-11*x^3-20*x^4)/(1-7*x-15*x^2+32*x^4+64*x^5)) \\ _Altug Alkan_, Jul 23 2018
%Y A185818 Cf. A185825.
%K A185818 nonn
%O A185818 1,2
%A A185818 _R. H. Hardin_, Feb 05 2011