A202526 Number of (n+2) X 4 binary arrays avoiding patterns 000 and 101 in rows, columns and nw-to-se diagonals.

198, 518, 1084, 2232, 4901, 10584, 22525, 48429, 104282, 223728, 480328, 1032213, 2217044, 4761249, 10227241, 21967770, 47183252, 101344728, 217680229, 467553984, 1004256629, 2157044997, 4633115818, 9951459720, 21374732936

Offset

1,1

Comments

Column 2 of A202532.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +2*a(n-3) -2*a(n-4) -2*a(n-5) +a(n-7) for n>9.

Empirical g.f.: x*(198 + 122*x + 48*x^2 - 332*x^3 - 203*x^4 + 46*x^5 + 97*x^6 + 11*x^7 + 4*x^8) / ((1 - x)*(1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)). - Colin Barker, Jun 01 2018

Example

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

Crossrefs

Cf. A202532.

Sequence in context: A055971 A075293 A083264 * A221219 A238765 A066218

Adjacent sequences: A202523 A202524 A202525 * A202527 A202528 A202529

Keyword

nonn

Author

R. H. Hardin, Dec 20 2011

Status

approved