A208634 Number of n X 5 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

16, 47, 150, 494, 1652, 5572, 18888, 64216, 218704, 745616, 2543520, 8679776, 29625920, 101131840, 345250944, 1178690944, 4024163584, 13739075840, 46907582976, 160151393792, 546788836352, 1866849412096, 6373813684224

Offset

1,1

Comments

Column 5 of A208637.

Links

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

Formula

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

Conjectures from Colin Barker, Jul 05 2018: (Start)

G.f.: x*(16 - 49*x + 28*x^2) / ((1 - 2*x)*(1 - 4*x + 2*x^2)).

a(n) = (3*2^(1+n) + (11-2*sqrt(2))*(2-sqrt(2))^n + (2+sqrt(2))^n*(11+2*sqrt(2))) / 4.

(End)

Example

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

Crossrefs

Cf. A208637.

Sequence in context: A292171 A204609 A233063 * A333602 A083307 A235765

Adjacent sequences: A208631 A208632 A208633 * A208635 A208636 A208637

Keyword

nonn

Author

R. H. Hardin, Feb 29 2012

Status

approved