A209647 Number of n X 5 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically.

14, 196, 798, 2156, 4690, 8904, 15386, 24808, 37926, 55580, 78694, 108276, 145418, 191296, 247170, 314384, 394366, 488628, 598766, 726460, 873474, 1041656, 1232938, 1449336, 1692950, 1965964, 2270646, 2609348, 2984506, 3398640, 3854354, 4354336

Offset: 1

Author

R. H. Hardin, Mar 11 2012

Keywords

• nonn

Comments

Column 5 of A209650.

Examples

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

Links

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

Crossrefs

Cf. A209650.

Programs

Maple

seq(7/2*n^4+21*n^3-7/2*n^2-7*n, n=1..50); # Robert Israel, Mar 07 2018

Formula

Empirical: a(n) = (7/2)*n^4 + 21*n^3 - (7/2)*n^2 - 7*n.

Conjectures from Colin Barker, Mar 07 2018: (Start)

G.f.: 14*x*(1 + 9*x - 3*x^2 - x^3) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Empirical formula (and thus Barker's conjectures) proved by Robert Israel, Mar 07 2018: see link.