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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. 1
8, 42, 256, 1682, 11448, 79162, 551216, 3849762, 26922088, 188375882, 1318394976, 9228056242, 64594267928, 452153498202, 3165055355536, 22155330093122, 155087138464968, 1085609452694122, 7599264619176896, 53194847685192402 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 2 08:36 EST 2022. Contains 358493 sequences. (Running on oeis4.)