A297301 Number of 4 X n 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 2 neighboring 1s.

1, 1, 5, 10, 21, 50, 130, 332, 840, 2128, 5408, 13772, 35102, 89465, 227961, 580788, 1479748, 3770356, 9606981, 24478804, 62372090, 158923930, 404938148, 1031783666, 2628989168, 6698674670, 17068245866, 43489945955, 110812526805

Offset

1,3

Comments

Row 4 of A297299.

Links

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

Robert Israel, Maple-assisted proof of empirical formula

Formula

Empirical: a(n) = 4*a(n-1) - 6*a(n-2) + 7*a(n-3) - 4*a(n-4) + 3*a(n-5) + a(n-6) - 5*a(n-7) + 4*a(n-8) - 2*a(n-9) - a(n-10) - 5*a(n-12) - 3*a(n-13) for n > 16.

Formula verified by Robert Israel, May 25 2018: see link.

Example

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

Crossrefs

Cf. A297299.

Sequence in context: A372054 A295952 A132174 * A132461 A255150 A266580

Adjacent sequences: A297298 A297299 A297300 * A297302 A297303 A297304

Keyword

nonn

Author

R. H. Hardin, Dec 27 2017

Status

approved