A296572 Number of n X 2 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0, 1 or 3 neighboring 1s.

4, 11, 31, 90, 254, 728, 2078, 5931, 16941, 48360, 138093, 394288, 1125795, 3214477, 9178177, 26206271, 74826094, 213649101, 610027119, 1741795342, 4973305753, 14200157940, 40545363081, 115768182159, 330550053876, 943811471644

Offset

1,1

Links

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

Formula

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

Empirical g.f.: x*(4 + 7*x + 4*x^2 + 3*x^3 + 3*x^4 - 6*x^5 - 7*x^6 + x^8) / (1 - x - 4*x^2 - 3*x^3 - x^4 - 4*x^5 + x^6 + 6*x^7 + x^8 - x^9). - Colin Barker, Feb 23 2019

Example

Some solutions for n=5:
..0..0. .1..0. .1..0. .0..0. .0..1. .1..1. .0..1. .0..0. .1..0. .0..1
..0..0. .0..0. .0..0. .0..0. .0..1. .0..0. .1..0. .1..1. .0..0. .0..1
..0..0. .0..1. .1..0. .1..0. .0..0. .1..1. .0..1. .0..0. .1..0. .1..1
..0..0. .0..0. .0..0. .1..0. .0..0. .0..0. .1..0. .1..0. .0..1. .1..0
..0..1. .0..0. .1..0. .0..0. .1..1. .0..0. .0..0. .0..0. .0..1. .1..0

Crossrefs

Column 2 of A296578.

Sequence in context: A077995 A276293 A282856 * A176573 A134597 A076730

Adjacent sequences: A296569 A296570 A296571 * A296573 A296574 A296575

Keyword

nonn

Author

R. H. Hardin, Dec 15 2017

Status

approved