A279710 Number of 3 X n 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

4, 5, 11, 22, 47, 102, 224, 494, 1089, 2400, 5289, 11661, 25718, 56728, 125125, 275973, 608663, 1342423, 2960792, 6530255, 14402991, 31766847, 70063951, 154530760, 340828154, 751720173, 1657971361, 3656771426, 8065263401, 17788497730

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + 4*a(n-4) - a(n-5) - a(n-7) - a(n-8).

Empirical g.f.: x*(4 - 7*x + 4*x^2 + 3*x^3 - 8*x^4 - 5*x^6) / ((1 - x)*(1 + x)*(1 - 2*x - x^3)*(1 - x + x^2 + x^3)). - Colin Barker, Feb 11 2019

Example

Some solutions for n=4:
..0..1..0..1. .0..1..0..1. .0..1..1..0. .0..1..1..0. .0..1..0..1
..0..1..0..0. .0..1..1..0. .0..0..0..1. .0..0..1..0. .1..0..1..0
..0..1..1..0. .0..0..1..0. .1..1..0..1. .0..1..0..1. .1..0..1..0

Crossrefs

Row 3 of A279709.

Sequence in context: A000286 A227620 A036539 * A303956 A000769 A246495

Adjacent sequences: A279707 A279708 A279709 * A279711 A279712 A279713

Keyword

nonn

Author

R. H. Hardin, Dec 17 2016

Status

approved