A280600 Number of n X 4 0..1 arrays with no element equal to more than two of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

8, 50, 116, 302, 726, 1709, 3996, 9346, 21891, 51367, 120680, 283746, 667466, 1570516, 3695871, 8698086, 20471383, 48181359, 113400534, 266902849, 628191882, 1478536037, 3479939872, 8190523786, 19277542258, 45372392065, 106790273799

Offset

1,1

Comments

Column 4 of A280604.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 4*a(n-2) + 2*a(n-5) - 3*a(n-7) + 2*a(n-8) + a(n-9) - a(n-10) for n>13.

Empirical g.f.: x*(8 + 18*x - 52*x^2 + 38*x^3 - 18*x^4 - 3*x^5 - 36*x^6 - 10*x^7 + 21*x^8 - 25*x^9 - 10*x^10 + 10*x^11 - x^12) / ((1 - x)^3*(1 + x + x^2)*(1 - 2*x - x^2 + x^3 - x^4 - x^5)). - Colin Barker, Mar 22 2018

Example

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

Crossrefs

Cf. A280604.

Sequence in context: A076286 A299049 A299811 * A282774 A258635 A300494

Adjacent sequences: A280597 A280598 A280599 * A280601 A280602 A280603

Keyword

nonn

Author

R. H. Hardin, Jan 06 2017

Status

approved