A296720 Number of n X 3 0..1 arrays with each 1 adjacent to 0, 2 or 4 king-move neighboring 1s.

5, 21, 69, 258, 963, 3493, 12860, 47305, 173498, 637397, 2341283, 8597415, 31576458, 115970574, 425911328, 1564226500, 5744847726, 21098720647, 77488048294, 284585727060, 1045180704781, 3838572624574, 14097695093525, 51775756521020

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + 3*a(n-2) + 4*a(n-3) - 19*a(n-4) - 14*a(n-5) + 9*a(n-6) + 14*a(n-7) + 6*a(n-8) - 3*a(n-9) - 2*a(n-10).

Empirical g.f.: x*(5 + 6*x - 9*x^2 - 32*x^3 - 7*x^4 + 23*x^5 + 20*x^6 + 3*x^7 - 5*x^8 - 2*x^9) / ((1 - x)*(1 - 2*x - 5*x^2 - 9*x^3 + 10*x^4 + 24*x^5 + 15*x^6 + x^7 - 5*x^8 - 2*x^9)). - Colin Barker, Feb 24 2019

Example

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

Crossrefs

Column 3 of A296725.

Sequence in context: A335982 A271282 A203287 * A099899 A269566 A271492

Adjacent sequences: A296717 A296718 A296719 * A296721 A296722 A296723

Keyword

nonn

Author

R. H. Hardin, Dec 19 2017

Status

approved