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

1,1

Comments

Column 1 of A203091.

Links

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

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

Example

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

Crossrefs

Cf. A203091.

Sequence in context: A063369 A038863 A203091 * A202378 A202371 A195751

Adjacent sequences: A203081 A203082 A203083 * A203085 A203086 A203087

Keyword

nonn

Author

R. H. Hardin, Dec 29 2011

Status

approved