A202400 Number of (n+2) X 4 binary arrays avoiding patterns 000 and 010 in rows and columns.

441, 2401, 14161, 83521, 485809, 2825761, 16475481, 96059601, 559842921, 3262808641, 19017237409, 110841719041, 646031745121, 3765342321601, 21946029946281, 127910874833361, 745519173814809, 4345203949621921

Offset

1,1

Comments

Column 2 of A202406.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 6*a(n-2) + 30*a(n-3) - 30*a(n-5) + 6*a(n-6) - 6*a(n-7) + a(n-8).

Empirical g.f.: x*(441 - 245*x + 2401*x^2 - 269*x^3 - 2381*x^4 + 433*x^5 - 477*x^6 + 81*x^7) / ((1 - x)*(1 + x)*(1 - 6*x + x^2)*(1 + 6*x^2 + x^4)). - Colin Barker, May 28 2018

Example

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

Crossrefs

Cf. A202406.

Sequence in context: A057950 A343827 A250808 * A014793 A264305 A321337

Adjacent sequences: A202397 A202398 A202399 * A202401 A202402 A202403

Keyword

nonn

Author

R. H. Hardin, Dec 19 2011

Status

approved