A203455 - OEIS

%I #8 Jun 27 2018 13:15:27

%S 1,9,84,543,3748,29677,237999,1882149,14936068,119307906,954802767,

%T 7642229473,61191946032,490168235993,3927147409735,31465890290038,

%U 252129334037581,2020326252175096,16189287109355756,129729279431146577

%N Number of nX3 0..2 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors

%C Column 3 of A203460

%H R. H. Hardin, <a href="/A203455/b203455.txt">Table of n, a(n) for n = 1..210</a>

%H Robert Israel, <a href="/A203455/a203455.pdf">Maple-assisted proof of formula</a>

%F Empirical: a(n) = 18*a(n-1) -133*a(n-2) +640*a(n-3) -2309*a(n-4) +5762*a(n-5) -9918*a(n-6) +8864*a(n-7) +2970*a(n-8) -18151*a(n-9) +23183*a(n-10) +21799*a(n-11) -75109*a(n-12) +56329*a(n-13) -9892*a(n-14) -115814*a(n-15) +105665*a(n-16) +64162*a(n-17) -38348*a(n-18) +8767*a(n-19) +54790*a(n-20) -95246*a(n-21) -139155*a(n-22) +81259*a(n-23) +104482*a(n-24) +18968*a(n-25) -2909*a(n-26) -41630*a(n-27) -37578*a(n-28) +6670*a(n-29) +17693*a(n-30) +5629*a(n-31) -713*a(n-32) -928*a(n-33) -300*a(n-34) -52*a(n-35) -4*a(n-36).

%F Empirical formula verified (see link). - _Robert Israel_, Jun 27 2018

%e Some solutions for n=5

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

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_ Jan 02 2012