A203455 Number of nX3 0..2 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors

1, 9, 84, 543, 3748, 29677, 237999, 1882149, 14936068, 119307906, 954802767, 7642229473, 61191946032, 490168235993, 3927147409735, 31465890290038, 252129334037581, 2020326252175096, 16189287109355756, 129729279431146577

Offset

1,2

Comments

Column 3 of A203460

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Robert Israel, Maple-assisted proof of formula

Formula

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).

Empirical formula verified (see link). - Robert Israel, Jun 27 2018

Example

Some solutions for n=5
..1..1..0....0..0..0....2..2..2....0..1..1....1..1..0....0..2..2....0..2..2
..1..1..0....0..1..1....2..1..2....2..2..1....1..1..0....2..2..2....2..2..2
..1..1..1....0..1..1....2..1..2....2..2..1....0..0..0....2..1..0....2..1..1
..0..2..2....2..2..0....2..2..2....2..2..1....1..1..1....2..2..1....2..2..1
..0..2..2....2..2..0....0..2..2....2..2..1....1..1..1....2..2..1....2..2..0

Crossrefs

Sequence in context: A321294 A242596 A180807 * A272582 A037595 A037686

Adjacent sequences: A203452 A203453 A203454 * A203456 A203457 A203458

Keyword

nonn

Author

R. H. Hardin Jan 02 2012

Status

approved