A237629 Number of (n+1) X (n+1) 0..2 arrays with the upper median of every 2 X 2 subblock differing from its horizontal and vertical neighbors by exactly one.

81, 636, 1310, 2012, 4622, 9368, 18344, 44292, 102536, 211268, 402152, 1015572, 2337608, 4914788, 9150632, 23921652, 54827528, 116999108, 214315112, 574558932, 1312885448, 2831048228, 5126666792, 13988255412, 31897292168, 69273334148

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..36

Formula

Empirical: a(n) = 4*a(n-2) + 25*a(n-4) - 100*a(n-6) for n>11.

Empirical g.f.: x*(81 + 636*x + 986*x^2 - 532*x^3 - 2643*x^4 - 14580*x^5 - 24794*x^6 + 20120*x^7 + 44610*x^8 + 1100*x^9 - 4392*x^10) / ((1 - 2*x)*(1 + 2*x)*(1 - 5*x^2)*(1 + 5*x^2)). - Colin Barker, Oct 23 2018

Example

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

Crossrefs

Diagonal of A237637.

Sequence in context: A322240 A185856 A185848 * A236720 A187441 A187433

Adjacent sequences: A237626 A237627 A237628 * A237630 A237631 A237632

Keyword

nonn

Author

R. H. Hardin, Feb 10 2014

Status

approved