A281465 Number of n X 4 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.

8, 37, 39, 96, 207, 405, 897, 1975, 4154, 8884, 19297, 41447, 88670, 190913, 411053, 882410, 1895974, 4078246, 8765802, 18835918, 40491783, 87045948, 187087510, 402129300, 864407625, 1858020929, 3993687963, 8584396666, 18452096569

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + a(n-2) + 4*a(n-3) + a(n-4) - 4*a(n-5) - 5*a(n-6) + 3*a(n-8) for n>10.

Empirical g.f.: x*(8 + 29*x - 6*x^2 - 12*x^3 - 84*x^4 - 59*x^5 + 50*x^6 + 90*x^7 + 10*x^8 - 41*x^9) / ((1 - x)*(1 - x^2 - 5*x^3 - 6*x^4 - 2*x^5 + 3*x^6 + 3*x^7)). - Colin Barker, Feb 19 2019

Example

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

Crossrefs

Column 4 of A281469.

Sequence in context: A050536 A261846 A110215 * A302619 A302411 A303178

Adjacent sequences: A281462 A281463 A281464 * A281466 A281467 A281468

Keyword

nonn

Author

R. H. Hardin, Jan 22 2017

Status

approved