A317767 Number of nX2 0..1 arrays with every element unequal to 0, 1 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

2, 3, 4, 7, 11, 18, 30, 49, 81, 134, 221, 365, 603, 996, 1645, 2717, 4488, 7413, 12244, 20224, 33405, 55176, 91136, 150533, 248641, 410689, 678350, 1120456, 1850698, 3056865, 5049136, 8339843, 13775223, 22753039, 37582027, 62075608, 102532550

Offset

1,1

Comments

Column 2 of A317773.

Links

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

Formula

Empirical: a(n) = a(n-1) +2*a(n-3) -a(n-6)

Empirical: G.f.: -x*(x-1)*(x^4+3*x^3+4*x^2+3*x+2)/(1-x-2*x^3+x^6) . - R. J. Mathar, May 09 2023

Example

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

Crossrefs

Cf. A317773.

Sequence in context: A254729 A293544 A080074 * A018064 A226161 A188624

Adjacent sequences: A317764 A317765 A317766 * A317768 A317769 A317770

Keyword

nonn

Author

R. H. Hardin, Aug 06 2018

Status

approved