A235895 Number of (n+1) X (1+1) 0..2 arrays with the minimum plus the maximum equal to the lower median plus the upper median in every 2 X 2 subblock.

33, 125, 473, 1797, 6849, 26189, 100457, 386517, 1491537, 5771933, 22396025, 87120549, 339708129, 1327583213, 5199036809, 20399760501, 80187289713, 315721128509, 1244976918425, 4916128826181, 19437363570945, 76940441387405

Offset

1,1

Links

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

Formula

Empirical: a(n) = 7*a(n-1) -10*a(n-2) -8*a(n-3).

Conjectures from Colin Barker, Oct 20 2018: (Start)

G.f.: x*(33 - 106*x - 72*x^2) / ((1 - 4*x)*(1 - 3*x - 2*x^2)).

a(n) = 4^(1+n) + (2^(-1-n)*((3-sqrt(17))^n*(-19+5*sqrt(17)) + (3+sqrt(17))^n*(19+5*sqrt(17)))) / sqrt(17).

(End)

Example

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

Crossrefs

Column 1 of A235902.

Sequence in context: A301633 A039440 A235902 * A010020 A007419 A158575

Adjacent sequences: A235892 A235893 A235894 * A235896 A235897 A235898

Keyword

nonn

Author

R. H. Hardin, Jan 16 2014

Status

approved