A197174 - OEIS

%I #9 May 11 2018 10:43:25

%S 1,5,10,23,58,144,363,917,2321,5878,14889,37722,95576,242163,613583,

%T 1554685,3939236,9981179,25290188,64079982,162365107,411398825,

%U 1042397613,2641215094,6692280455,16956823380,42965004446,108864235075

%N Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,2,1,0,0 for x=0,1,2,3,4.

%C Every 0 is next to 0 2's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 0's.

%C Column 2 of A197180.

%H R. H. Hardin, <a href="/A197174/b197174.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) +a(n-2) +2*a(n-3) -a(n-4) -4*a(n-5) -2*a(n-6) +a(n-7) +a(n-8).

%F Empirical g.f.: x*(1 + x)*(1 + 2*x - 3*x^2 - x^3 - 6*x^4 + 3*x^6) / (1 - 2*x - x^2 - 2*x^3 + x^4 + 4*x^5 + 2*x^6 - x^7 - x^8). - _Colin Barker_, May 11 2018

%e Some solutions for n=4:

%e ..0..0....0..0....1..2....1..2....0..0....1..2....1..0....2..1....2..1....0..1

%e ..0..3....0..0....0..1....0..1....0..0....0..1....2..1....1..0....1..0....1..2

%e ..3..0....0..1....0..0....3..0....3..0....1..0....2..1....0..1....1..0....1..2

%e ..0..0....1..2....0..0....0..0....0..0....2..1....1..0....1..2....2..1....0..1

%Y Cf. A197180.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 11 2011