A197524 - OEIS

%I #9 May 13 2018 06:04:58

%S 1,3,32,69,308,1444,5048,20265,83277,322864,1280598,5112008,20189827,

%T 80032884,317712722,1258773307,4990157041,19788837323,78445935632,

%U 310998937948,1233039388705,4888402255720,19380385472489,76835860723308

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

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

%C Column 3 of A197529.

%H R. H. Hardin, <a href="/A197524/b197524.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) +2*a(n-2) +19*a(n-3) +10*a(n-4) +21*a(n-5) +31*a(n-6) -99*a(n-7) -9*a(n-8) +16*a(n-9).

%F Empirical g.f.: x*(1 + x + 24*x^2 - 20*x^3 + 39*x^4 + 31*x^5 - 181*x^6 + 73*x^7) / (1 - 2*x - 2*x^2 - 19*x^3 - 10*x^4 - 21*x^5 - 31*x^6 + 99*x^7 + 9*x^8 - 16*x^9). - _Colin Barker_, May 13 2018

%e Some solutions for n=4:

%e ..0..0..0....0..3..0....0..3..0....0..0..0....0..0..0....0..0..0....0..0..0

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

%e ..1..4..1....0..0..0....3..0..0....0..0..0....3..0..0....1..4..1....0..0..3

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

%Y Cf. A197529.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 16 2011