A197745 - OEIS

%I #10 Jan 16 2024 00:58:24

%S 2,12,66,212,921,4086,17332,75122,326124,1408419,6097753,26404858,

%T 114255411,494519798,2140532037,9264510866,40098753497,173557720814,

%U 751196491106,3251349837567,14072600064116,60909443628883,263630086389334,1141051836433576,4938735140721662

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

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

%H R. H. Hardin, <a href="/A197745/b197745.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) +3*a(n-2) +26*a(n-3) +20*a(n-4) +24*a(n-5) -62*a(n-6) -166*a(n-7) -99*a(n-8) +128*a(n-9) +383*a(n-10) +75*a(n-11) -563*a(n-12) -540*a(n-13) +86*a(n-14) +624*a(n-15) +663*a(n-16) +220*a(n-17) -159*a(n-18) -266*a(n-19) -229*a(n-20) -125*a(n-21) -30*a(n-22) +12*a(n-23) +4*a(n-24).

%e Some solutions for n=4:

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

%e ..3..1..0....2..2..0....0..4..0....0..0..2....2..0..0....2..2..2....0..1..0

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

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

%Y Column 3 of A197750.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 17 2011