A203829 Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.

225, 1971, 17289, 151659, 1330353, 11669859, 102368025, 897972507, 7877016513, 69097203603, 606120799401, 5316892787403, 46639793487825, 409124355815619, 3588839615364921, 31481307826653051, 276154091209147617

Offset

1,1

Comments

Column 2 of A203835.

Links

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

Formula

Empirical: a(n) = 9*a(n-1) -2*a(n-2).

Conjectures from Colin Barker, Jun 05 2018: (Start)

G.f.: 9*x*(25 - 6*x) / (1 - 9*x + 2*x^2).

a(n) = (9*2^(-1-n)*((9-sqrt(73))^n*(-23+3*sqrt(73)) + (9+sqrt(73))^n*(23+3*sqrt(73)))) / sqrt(73).

(End)

Example

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

Crossrefs

Cf. A203835.

Sequence in context: A272674 A242381 A076395 * A105925 A014771 A184878

Adjacent sequences: A203826 A203827 A203828 * A203830 A203831 A203832

Keyword

nonn

Author

R. H. Hardin, Jan 06 2012

Status

approved