A296014 Number of n X 3 0..1 arrays with each 1 adjacent to 1 or 4 king-move neighboring 1s.

3, 13, 30, 91, 280, 785, 2319, 6816, 19796, 57991, 169568, 495194, 1447954, 4232103, 12368507, 36153433, 105669553, 308852290, 902733635, 2638539016, 7712024753, 22541039139, 65883825698, 192567918338, 562845326527, 1645106908766

Offset

1,1

Comments

Column 3 of A296019.

Links

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

Robert Israel, Maple-assisted proof of formula

Formula

Empirical: a(n) = a(n-1) + 3*a(n-2) + 11*a(n-3) - 3*a(n-4) - 11*a(n-5) - 27*a(n-6) + a(n-7) + 6*a(n-8) + 7*a(n-9) + a(n-10).

Empirical formula confirmed by Robert Israel, Dec 03 2017 (see link).

Example

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

Crossrefs

Cf. A296019.

Sequence in context: A330451 A022264 A288541 * A273337 A273769 A097955

Adjacent sequences: A296011 A296012 A296013 * A296015 A296016 A296017

Keyword

nonn

Author

R. H. Hardin, Dec 02 2017

Status

approved