A231126 Number of (n+1) X (3+1) white-square subarrays of 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

6, 40, 308, 2260, 16812, 124644, 924900, 6862052, 50913012, 377747700, 2802692276, 20794524084, 154284599124, 1144711823796, 8493168927828, 63014915159220, 467538037568404, 3468890119531892, 25737368287958996, 190957944347003188

Offset

1,1

Comments

Column 3 of A231131.

Links

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

Formula

Empirical: a(n) = 7*a(n-1) + 8*a(n-2) - 32*a(n-3) - 38*a(n-4) + 40*a(n-5) + 56*a(n-6) - 16*a(n-7) - 16*a(n-8).

Empirical g.f.: 2*x*(3 - x - 10*x^2 - 12*x^3 + 18*x^4 + 8*x^5 - 8*x^6) / (1 - 7*x - 8*x^2 + 32*x^3 + 38*x^4 - 40*x^5 - 56*x^6 + 16*x^7 + 16*x^8). - Colin Barker, Mar 18 2018

Example

Some solutions for n=5:
..0..x..0..x....0..x..0..x....0..x..1..x....0..x..1..x....0..x..0..x
..x..1..x..2....x..1..x..2....x..2..x..0....x..2..x..2....x..1..x..0
..2..x..1..x....2..x..1..x....0..x..1..x....0..x..2..x....2..x..2..x
..x..0..x..2....x..0..x..0....x..0..x..1....x..1..x..0....x..0..x..2
..1..x..2..x....1..x..1..x....1..x..2..x....1..x..2..x....0..x..1..x
..x..2..x..1....x..0..x..0....x..1..x..1....x..2..x..1....x..2..x..2

Crossrefs

Cf. A231131.

Sequence in context: A358598 A083805 A181571 * A341587 A006387 A014481

Adjacent sequences: A231123 A231124 A231125 * A231127 A231128 A231129

Keyword

nonn

Author

R. H. Hardin, Nov 04 2013

Status

approved