A231765 Number of (1+1) X (n+1) 0..1 arrays with no element having a strict majority of its horizontal, diagonal and antidiagonal neighbors equal to one.

9, 33, 100, 315, 961, 3024, 9409, 29319, 91204, 284279, 885481, 2758192, 8590761, 26760591, 83356900, 259648623, 808776721, 2519272112, 7847302225, 24443615655, 76139572356, 237167776135, 738755721081, 2301155717168, 7167887098681

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + a(n-3) + 7*a(n-4) - 20*a(n-5) - 2*a(n-6) - 4*a(n-8) + 8*a(n-9).

Empirical g.f.: x*(9 + 6*x + x^2 + 6*x^3 - 80*x^4 - 10*x^5 - 8*x^7 + 32*x^8) / ((1 - 3*x - x^2 + 2*x^3)*(1 + x^2 - 6*x^4 - 4*x^6)). - Colin Barker, Oct 01 2018

Example

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

Crossrefs

Row 1 of A231764.

Sequence in context: A112888 A048479 A031880 * A220165 A036543 A147269

Adjacent sequences: A231762 A231763 A231764 * A231766 A231767 A231768

Keyword

nonn

Author

R. H. Hardin, Nov 13 2013

Status

approved