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A203455 Number of nX3 0..2 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors 1
1, 9, 84, 543, 3748, 29677, 237999, 1882149, 14936068, 119307906, 954802767, 7642229473, 61191946032, 490168235993, 3927147409735, 31465890290038, 252129334037581, 2020326252175096, 16189287109355756, 129729279431146577 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 5 01:51 EDT 2021. Contains 346456 sequences. (Running on oeis4.)