A203084 Number of (n+2) X 3 binary arrays avoiding patterns 000 and 101 in rows and columns.

98, 253, 621, 1575, 4000, 10057, 25384, 64140, 161819, 408415, 1031041, 2602296, 6568305, 16579362, 41847510, 105626421, 266611217, 672949667, 1698582936, 4287374163, 10821707646, 27314936026, 68945297129, 174023973205

Offset: 1

Author

R. H. Hardin, Dec 29 2011

Keywords

• nonn

Comments

Column 1 of A203091.

Examples

			Some solutions for n=3:
  1 0 0    1 1 0    1 1 0    0 1 0    0 0 1    1 1 1    1 0 0
  1 1 0    1 1 0    1 1 1    1 0 0    1 1 1    1 1 0    1 1 0
  1 1 1    1 1 1    1 1 1    0 0 1    1 0 0    1 1 0    0 1 1
  1 1 1    0 1 1    1 1 1    0 1 1    1 0 0    0 1 1    0 1 1
  0 1 0    0 0 1    0 1 0    1 1 0    0 1 1    0 0 1    1 0 0
		

Links

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

Crossrefs

Cf. A203091.

Formula

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

Empirical g.f.: x*(98 + 155*x + 270*x^2 + 113*x^3 + 90*x^4 - 44*x^5 - 26*x^6 - 61*x^7 - 53*x^8 - 36*x^9) / (1 - x - x^2 - 6*x^3 - 2*x^4 - 3*x^5 + x^6 + x^8 + x^9 + x^10). - Colin Barker, Mar 03 2018