A281339 Number of n X 3 0..1 arrays with no element equal to more than three of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

4, 25, 68, 193, 544, 1539, 4355, 12332, 34907, 98797, 279622, 791433, 2240071, 6340292, 17945485, 50792619, 143762646, 406903731, 1151694633, 3259740340, 9226322979, 26114053785, 73912847850, 209201878257, 592122035615

Offset

1,1

Links

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

Formula

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

Empirical g.f.: x*(4 + 13*x - 3*x^2 + 18*x^3 + 30*x^4 - 3*x^5 + 16*x^6 + 9*x^7 + 4*x^8 + 4*x^9) / (1 - 3*x + x^2 + x^3 - 7*x^4 + x^5 - 2*x^6 - 2*x^7 - 2*x^9). - Colin Barker, Feb 18 2019

Example

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

Crossrefs

Column 3 of A281344.

Sequence in context: A376483 A302324 A303017 * A298282 A077205 A180569

Adjacent sequences: A281336 A281337 A281338 * A281340 A281341 A281342

Keyword

nonn

Author

R. H. Hardin, Jan 20 2017

Status

approved