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

Author

R. H. Hardin, Dec 27 2017

Keywords

• nonn

Comments

Row 4 of A297299.

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Robert Israel, Maple-assisted proof of empirical formula

Crossrefs

Cf. A297299.

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.