cp's OEIS Frontend

A196205 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,3,4,1 for x=0,1,2,3,4.

%I A196205 #8 Mar 01 2018 05:34:41
%S A196205 4,8,7,14,17,27,42,58,94,137,208,319,477,732,1108,1686,2573,3912,5975,
%T A196205 9113,13914,21268,32504,49733,76116,116561,178607,273786,419924,
%U A196205 644346,989153,1519164,2334105,3587703,5516702,8486022,13058268,20100879
%N A196205 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,3,4,1 for x=0,1,2,3,4.
%C A196205 Every 0 is next to 0 2's, every 1 is next to 1 0's, every 2 is next to 2 3's, every 3 is next to 3 4's, every 4 is next to 4 1's.
%C A196205 Column 3 of A196210.
%H A196205 R. H. Hardin, <a href="/A196205/b196205.txt">Table of n, a(n) for n = 1..200</a>
%F A196205 Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-4) + 3*a(n-5) - 2*a(n-6) + 2*a(n-7) - 2*a(n-8) + a(n-9).
%F A196205 Empirical g.f.: x*(4 - 4*x - 9*x^2 + 9*x^3 - 3*x^4 + 8*x^5 - 7*x^6 + x^7 + 2*x^8) / ((1 - x)*(1 - x - x^3)*(1 - x - x^2 + x^4 - x^5)). - _Colin Barker_, Mar 01 2018
%e A196205 Some solutions for n=4:
%e A196205 ..1..1..0....1..0..0....1..0..1....1..0..0....1..1..1....1..1..1....0..0..0
%e A196205 ..0..1..1....1..0..0....1..0..1....1..1..1....0..0..0....0..0..0....0..0..0
%e A196205 ..0..1..1....1..0..0....1..0..1....0..1..1....0..0..0....0..0..0....0..0..0
%e A196205 ..1..1..0....1..0..0....1..0..1....1..1..0....0..0..0....1..1..1....1..1..1
%Y A196205 Cf. A196210.
%K A196205 nonn
%O A196205 1,1
%A A196205 _R. H. Hardin_, Sep 29 2011