A204565 Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..3 introduced in row major order.

8, 42, 256, 1682, 11448, 79162, 551216, 3849762, 26922088, 188375882, 1318394976, 9228056242, 64594267928, 452153498202, 3165055355536, 22155330093122, 155087138464968, 1085609452694122, 7599264619176896, 53194847685192402

Offset

1,1

Comments

Column 1 of A204572.

Links

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

Formula

Empirical: a(n) = 11*a(n-1) - 31*a(n-2) + 21*a(n-3).

Conjectures from Colin Barker, Jun 07 2018: (Start)

G.f.: 2*x*(4 - 23*x + 21*x^2) / ((1 - x)*(1 - 3*x)*(1 - 7*x)).

a(n) = 1/3 + 3^n + (2*7^n)/3.

(End)

Example

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

Crossrefs

Cf. A204572.

Sequence in context: A346980 A047759 A047772 * A020068 A266474 A238723

Adjacent sequences: A204562 A204563 A204564 * A204566 A204567 A204568

Keyword

nonn

Author

R. H. Hardin, Jan 16 2012

Status

approved