A252715 Number of (n+2) X (4+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.

96, 63, 70, 97, 135, 178, 257, 368, 492, 722, 1047, 1406, 2077, 3031, 4074, 6037, 8844, 11884, 17642, 25919, 34806, 51737, 76191, 102242, 152137, 224512, 301068, 448402, 662943, 888430, 1324277, 1961135, 2626650, 3918077, 5810940, 7778828, 11610922

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*(96 - 33*x + 7*x^2 - 549*x^3 + 236*x^4 + x^5 + 877*x^6 - 447*x^7 - 64*x^8 - 262*x^9 + 138*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..1..1..0..1..1....0..1..1..0..1..1....0..1..0..0..1..0....0..0..1..0..0..2
..0..2..0..0..3..0....1..0..1..1..0..1....2..2..0..2..2..0....0..3..3..0..3..3
..0..0..2..0..0..3....2..2..1..2..2..1....3..0..0..1..0..0....0..1..0..0..1..0
..0..1..1..0..1..1....0..1..1..0..1..1....0..3..0..0..1..0....0..0..1..0..0..1
..0..2..0..0..2..0....1..0..1..1..0..1....2..2..0..2..2..0....0..3..3..0..3..3
..0..0..2..0..0..2....2..2..1..2..2..1....1..0..0..3..0..0....0..2..0..0..1..0

Crossrefs

Column 4 of A252719.

Sequence in context: A057400 A216404 A033416 * A050277 A090221 A334654

Adjacent sequences: A252712 A252713 A252714 * A252716 A252717 A252718

Keyword

nonn

Author

R. H. Hardin, Dec 20 2014

Status

approved