A281464 Number of n X 3 0..1 arrays with no element equal to more than two of its horizontal, diagonal or antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

4, 17, 24, 60, 133, 283, 634, 1419, 3092, 6849, 15213, 33509, 74017, 163898, 361980, 799660, 1768383, 3908128, 8635736, 19089245, 42191413, 93242838, 206088583, 455499706, 1006707139, 2224999897, 4917670483, 10868814633, 24021891696

Offset

1,1

Links

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

Formula

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

Empirical g.f.: x*(4 + 9*x - 10*x^2 - 26*x^4 + 12*x^5 + 12*x^6 - 24*x^7 + 16*x^8) / (1 - 2*x - 3*x^3 + 3*x^4 + 4*x^5 - 4*x^6 + 4*x^7). - Colin Barker, Feb 19 2019

Example

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

Crossrefs

Column 3 of A281469.

Sequence in context: A041529 A042033 A372749 * A192197 A009226 A273022

Adjacent sequences: A281461 A281462 A281463 * A281465 A281466 A281467

Keyword

nonn

Author

R. H. Hardin, Jan 22 2017

Status

approved