A203650 1/25 the number of (n+1) X 3 0..4 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.

81, 1517, 28057, 519445, 9616161, 178019197, 3295578857, 61009378085, 1129435635441, 20908668388877, 387071560403257, 7165659241743925, 132654210800937921, 2455760042384774557, 45462238622967429257

Offset

1,1

Comments

Column 2 of A203656.

Links

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

Formula

Empirical: a(n) = 17*a(n-1) +28*a(n-2).

Conjectures from Colin Barker, Jun 04 2018: (Start)

G.f.: x*(81 + 140*x) / (1 - 17*x - 28*x^2).

a(n) = (2^(-1-n)*((17-sqrt(401))^n*(-77+5*sqrt(401)) + (17+sqrt(401))^n*(77+5*sqrt(401))))/sqrt(401).

(End)

Example

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

Crossrefs

Cf. A203656.

Sequence in context: A237771 A110921 A236867 * A284057 A237559 A223279

Adjacent sequences: A203647 A203648 A203649 * A203651 A203652 A203653

Keyword

nonn

Author

R. H. Hardin, Jan 04 2012

Status

approved