A316118 Number of nX3 0..1 arrays with every element unequal to 0, 2, 3, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 7, 13, 23, 47, 144, 391, 1118, 3330, 10129, 30953, 95037, 293116, 905585, 2799778, 8662028, 26809369, 82990751, 256933941, 795508636, 2463117879, 7626665518, 23615103348, 73122045417, 226416803035, 701083972797, 2170861196560

Offset

1,2

Comments

Column 3 of A316123.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) -7*a(n-3) -10*a(n-4) +7*a(n-5) +24*a(n-6) +20*a(n-7) -38*a(n-8) -69*a(n-9) +22*a(n-10) +115*a(n-11) +43*a(n-12) -92*a(n-13) -56*a(n-14) +18*a(n-15) +16*a(n-16) +4*a(n-17) for n>19

Example

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

Crossrefs

Cf. A316123.

Sequence in context: A270792 A304671 A075642 * A265766 A228727 A286916

Adjacent sequences: A316115 A316116 A316117 * A316119 A316120 A316121

Keyword

nonn

Author

R. H. Hardin, Jun 24 2018

Status

approved