A280064 Number of n X 3 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

1, 2, 5, 15, 39, 104, 281, 771, 2122, 5858, 16174, 44694, 123510, 341403, 943694, 2608709, 7211359, 19935055, 55108220, 152341402, 421132682, 1164181573, 3218268552, 8896600238, 24593808939, 67987267220, 187944382019, 519554527901

Offset

1,2

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + a(n-2) - 6*a(n-3) + 5*a(n-4) - 2*a(n-5) - 2*a(n-6) - a(n-7) for n>9.

Empirical g.f.: x*(1 + x)*(1 - 2*x + 4*x^3 - 8*x^4 + 2*x^5 - x^6 - x^7) / ((1 - x + x^2)*(1 - 2*x - 4*x^2 + 4*x^3 + 3*x^4 + x^5)). - Colin Barker, Feb 12 2019

Example

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

Crossrefs

Column 3 of A280069.

Sequence in context: A258121 A242823 A059840 * A148342 A148343 A148344

Adjacent sequences: A280061 A280062 A280063 * A280065 A280066 A280067

Keyword

nonn

Author

R. H. Hardin, Dec 25 2016

Status

approved