A252956 Number of (n+2) X (3+2) 0..4 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.

223, 155, 259, 443, 871, 1681, 2999, 6103, 11983, 21749, 44515, 88087, 161123, 330817, 656011, 1210571, 2483599, 4939057, 9174815, 18819943, 37462903, 70101461, 143554507, 286165735, 538738571, 1101824353, 2197577587, 4162662491

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 3*a(n-3) - 13*a(n-4) + 8*a(n-5) + 70*a(n-6) - 105*a(n-7) + 42*a(n-8) for n>10.

Empirical g.f.: x*(223 - 737*x + 85*x^2 + 386*x^3 + 2981*x^4 + 91*x^5 - 14137*x^6 + 16334*x^7 - 4830*x^8 - 420*x^9) / ((1 - x)^2*(1 - 2*x)*(1 - 3*x^2)*(1 - 7*x^3)). - Colin Barker, Dec 07 2018

Example

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

Crossrefs

Column 3 of A252961.

Sequence in context: A268017 A267978 A234623 * A163653 A178551 A105982

Adjacent sequences: A252953 A252954 A252955 * A252957 A252958 A252959

Keyword

nonn

Author

R. H. Hardin, Dec 25 2014

Status

approved