A259243 - OEIS

A259243

Number of (n+1) X (1+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0111.

9, 21, 48, 111, 255, 588, 1353, 3117, 7176, 16527, 38055, 87636, 201801, 464709, 1070112, 2464239, 5674575, 13067292, 30091017, 69292893, 159565944, 367444623, 846142455, 1948476324, 4486903689, 10332332661, 23793043728, 54790041711

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OFFSET

1,1

LINKS

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

FORMULA

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

Conjectures from Colin Barker, Dec 24 2018: (Start)

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

a(n) = (2^(-n)*((1-sqrt(13))^n*(-7+2*sqrt(13)) + (1+sqrt(13))^n*(7+2*sqrt(13)))) / sqrt(13).

(End)

EXAMPLE

Some solutions for n=4:

..1..0....1..1....1..0....0..1....1..0....1..1....1..1....1..0....0..1....0..1

..1..0....1..0....1..1....1..1....1..1....0..1....0..1....1..1....1..1....1..1

..1..1....1..0....0..1....0..1....0..0....1..1....0..1....0..1....1..0....0..0

..0..0....1..1....1..1....1..1....1..1....0..1....1..1....1..1....1..1....1..1

..1..1....0..1....0..0....0..1....0..0....0..1....0..0....1..0....1..0....0..0

CROSSREFS

Column 1 of A259250.

Sequence in context: A246318 A277715 A173391 * A241747 A133762 A160414

Adjacent sequences: A259240 A259241 A259242 * A259244 A259245 A259246

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jun 22 2015

STATUS

approved