A231538 Number of n X 2 0..1 arrays with no element less than a strict majority of its horizontal, vertical and antidiagonal neighbors.

2, 6, 20, 57, 164, 485, 1424, 4169, 12228, 35868, 105177, 308433, 904520, 2652574, 7778858, 22812126, 66898367, 196184665, 575326896, 1687191264, 4947820577, 14509871545, 42551335553, 124785126404, 365942162811, 1073154072467

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 4*a(n-2) + 5*a(n-3) - 8*a(n-4) + 3*a(n-5) - 2*a(n-6) + a(n-7) - a(n-8).

Empirical g.f.: x*(2 - 2*x + 4*x^2 - 9*x^3 + 2*x^4 - x^5 + x^6 - x^7) / (1 - 4*x + 4*x^2 - 5*x^3 + 8*x^4 - 3*x^5 + 2*x^6 - x^7 + x^8). - Colin Barker, Sep 29 2018

Example

Some solutions for n=7:
  0 1   1 0   1 1   0 1   1 1   1 0   0 1   0 0   0 0   1 0
  0 1   0 0   1 1   0 0   0 0   0 0   0 1   0 0   1 0   0 0
  0 0   0 1   0 0   1 0   0 0   0 1   0 1   0 0   0 0   1 1
  1 0   0 0   0 0   0 0   1 1   1 1   0 0   1 0   1 1   1 0
  0 1   0 1   1 0   0 1   1 1   1 1   1 0   1 0   1 1   0 0
  0 0   1 0   0 0   0 0   0 0   0 0   0 0   0 0   1 0   0 0
  0 0   0 0   0 1   0 0   0 0   0 0   0 1   0 1   0 0   0 0

Crossrefs

Column 2 of A231544.

Sequence in context: A327414 A110295 A027294 * A082045 A358301 A361732

Adjacent sequences: A231535 A231536 A231537 * A231539 A231540 A231541

Keyword

nonn

Author

R. H. Hardin, Nov 10 2013

Status

approved