A251212 Number of (n+1) X (1+1) 0..1 arrays with no 2 X 2 subblock having zero or two 1's.

9, 21, 49, 115, 269, 631, 1477, 3463, 8109, 19007, 44517, 104327, 244381, 572655, 1341525, 3143383, 7364173, 17254655, 40424581, 94714855, 221903869, 519914127, 1218099893, 2853948663, 6686519981, 15666114847, 36704297445, 85995716871

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) - 2*a(n-3).

Empirical g.f.: x*(9 + 12*x - 8*x^2) / (1 - x - 4*x^2 + 2*x^3). - Colin Barker, Nov 27 2018

Example

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

Crossrefs

Column 1 of A251219.

Sequence in context: A363634 A118130 A144482 * A176896 A347502 A134717

Adjacent sequences: A251209 A251210 A251211 * A251213 A251214 A251215

Keyword

nonn

Author

R. H. Hardin, Nov 30 2014

Status

approved