A196851 - OEIS

%I #7 Jan 20 2024 18:54:46

%S 4,38,206,1370,8767,56470,363685,2343584,15108610,97376923,627590184,

%T 4044924351,26070308556,168028055199,1082971243944,6979940126878,

%U 44986968132898,289949111595991,1868774104215258,12044584704922151

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

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

%C Column 3 of A196856.

%H R. H. Hardin, <a href="/A196851/b196851.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) +15*a(n-2) +56*a(n-3) +146*a(n-4) +360*a(n-5) +425*a(n-6) -1080*a(n-7) -2478*a(n-8) -3775*a(n-9) -9754*a(n-10) -17994*a(n-11) -19980*a(n-12) -14594*a(n-13) -14650*a(n-14) -19546*a(n-15) -5675*a(n-16) +14364*a(n-17) +18717*a(n-18) +4862*a(n-19) +1390*a(n-20) +267*a(n-21) +8378*a(n-22) -3292*a(n-23) +1287*a(n-24) -719*a(n-25) +281*a(n-26) -181*a(n-27) +42*a(n-28) -5*a(n-29) for n>31.

%e Some solutions for n=4

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

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

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

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

%Y Cf. A196856.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 06 2011