A252716 Number of (n+2) X (5+2) 0..3 arrays with every consecutive three elements in every row and diagonal having exactly two distinct values, and in every column and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order.

129, 69, 86, 112, 147, 214, 288, 383, 564, 768, 1027, 1518, 2080, 2789, 4126, 5680, 7629, 11284, 15600, 20981, 31014, 43056, 57979, 85638, 119392, 160967, 237556, 332608, 448971, 662014, 930912, 1258109, 1853454, 2617584, 3541861, 5213268

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + 6*a(n-3) - 6*a(n-4) - 10*a(n-6) + 10*a(n-7) + 3*a(n-9) - 3*a(n-10) for n>12.

Empirical g.f.: x*(129 - 60*x + 17*x^2 - 748*x^3 + 395*x^4 - 35*x^5 + 1208*x^6 - 715*x^7 - 51*x^8 - 367*x^9 + 219*x^10 + 24*x^11) / ((1 - x)*(1 - 3*x^3)*(1 - 3*x^3 + x^6)). - Colin Barker, Dec 05 2018

Example

Some solutions for n=4:
..0..0..1..0..0..1..0....0..1..0..0..1..0..0....0..1..1..0..1..1..2
..1..0..0..1..0..0..2....1..1..2..1..1..2..1....1..0..1..1..0..1..1
..3..0..3..3..0..3..3....3..1..1..2..1..1..2....3..3..1..3..3..1..3
..0..0..1..0..0..1..0....0..1..0..0..1..0..0....0..1..1..0..1..1..0
..1..0..0..1..0..0..1....1..1..3..1..1..2..1....1..0..1..1..0..1..1
..3..0..3..3..0..3..3....3..1..1..3..1..1..2....2..2..1..2..2..1..2

Crossrefs

Column 5 of A252719.

Sequence in context: A087929 A034062 A241311 * A337068 A298720 A025332

Adjacent sequences: A252713 A252714 A252715 * A252717 A252718 A252719

Keyword

nonn

Author

R. H. Hardin, Dec 20 2014

Status

approved