A316636 Number of nX3 0..1 arrays with every element unequal to 1, 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 16, 43, 122, 404, 1344, 4583, 15737, 53378, 182889, 626144, 2140598, 7328954, 25088547, 85860039, 293920208, 1006105675, 3443828176, 11788522574, 40352683838, 138128383567, 472821164301, 1618489337206, 5540161660167

Offset

1,2

Comments

Column 3 of A316641.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +5*a(n-2) +7*a(n-3) -15*a(n-4) -36*a(n-5) -3*a(n-6) -5*a(n-7) +39*a(n-8) +47*a(n-9) +67*a(n-10) +31*a(n-11) -69*a(n-12) -52*a(n-13) -53*a(n-14) +17*a(n-15) +15*a(n-16) -12*a(n-17) -8*a(n-18) -4*a(n-19) for n>21

Example

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

Crossrefs

Cf. A316641.

Sequence in context: A218067 A187729 A088800 * A187721 A253397 A258554

Adjacent sequences: A316633 A316634 A316635 * A316637 A316638 A316639

Keyword

nonn

Author

R. H. Hardin, Jul 09 2018

Status

approved