A196952 - OEIS

%I #9 May 10 2018 11:26:55

%S 3,9,26,87,282,919,2987,9722,31643,102962,335048,1090310,3548040,

%T 11545789,37571671,122263766,397863990,1294706917,4213164246,

%U 13710247872,44615134395,145184117131,472450174347,1537421386475,5002992156783

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

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

%C Column 3 of A196957.

%H R. H. Hardin, <a href="/A196952/b196952.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = a(n-1) +4*a(n-2) +8*a(n-3) +10*a(n-4) +a(n-5) -9*a(n-6) -6*a(n-7) +a(n-9) for n>10.

%F Empirical g.f.: x*(3 + 6*x + 5*x^2 + x^3 - 11*x^4 - 12*x^5 + 2*x^6 + 6*x^7 + 2*x^8 - x^9) / (1 - x - 4*x^2 - 8*x^3 - 10*x^4 - x^5 + 9*x^6 + 6*x^7 - x^9). - _Colin Barker_, May 10 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A196957.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 08 2011