A218227 Hilltop maps: number of n X 2 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal, vertical or antidiagonal neighbor in a random 0..2 n X 2 array.

3, 15, 61, 241, 961, 3839, 15327, 61185, 244257, 975105, 3892739, 15540287, 62038717, 247666113, 988713281, 3947063807, 15757159327, 62904498689, 251122418273, 1002511271425, 4002147065347, 15977058402447, 63782362573693

Offset

1,1

Comments

Column 2 of A218233.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + 3*a(n-2) + 3*a(n-3) + 3*a(n-4) + a(n-5) + a(n-6) + a(n-7) + a(n-8) + a(n-9).

Empirical g.f.: x*(3 + 6*x + 7*x^2 + 4*x^3 + x^4 + 2*x^5 + 3*x^6 + 2*x^7 + x^8) / (1 - 3*x - 3*x^2 - 3*x^3 - 3*x^4 - x^5 - x^6 - x^7 - x^8 - x^9). - Colin Barker, Jul 24 2018

Example

Some solutions for n=3:
..1..1....1..1....0..1....0..1....0..1....1..0....1..0....1..1....0..0....0..1
..1..0....0..0....0..0....0..1....1..1....1..1....0..0....0..0....1..0....1..0
..0..0....0..0....0..1....0..1....1..0....1..1....1..1....1..1....0..1....0..1

Crossrefs

Cf. A218233.

Sequence in context: A001655 A058749 A292483 * A072336 A356421 A122671

Adjacent sequences: A218224 A218225 A218226 * A218228 A218229 A218230

Keyword

nonn

Author

R. H. Hardin, Oct 24 2012

Status

approved