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A207142 Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having nonzero determinant and commuting with every horizontal or vertical neighbor. 1
50, 30, 80, 62, 159, 122, 315, 242, 628, 482, 1254, 962, 2506, 1922, 5010, 3842, 10018, 7682, 20034, 15362, 40066, 30722, 80130, 61442, 160258, 122882, 320514, 245762, 641026, 491522, 1282050, 983042, 2564098, 1966082, 5128194, 3932162, 10256386 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 1 of A207149.

LINKS

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

FORMULA

Empirical: a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) for n>8.

Conjectures from Colin Barker, Jun 19 2018: (Start)

G.f.: x*(50 - 20*x - 50*x^2 + 22*x^3 - 3*x^4 - x^5 - x^6 + x^7) / ((1 - x)*(1 - 2*x^2)).

a(n) = 15 * 2^(n/2) + 2 for n>5 and even.

a(n) = 313 * 2^((n-7)/2) + 2 for n>5 and odd.

(End)

EXAMPLE

Some solutions for n=4:

..2..0....2..1....1..1....2..1....1..1....0..2....0..1....2..1....0..1....1..0

..0..2....2..0....2..0....1..2....1..0....1..0....2..0....1..0....2..0....0..1

..1..0....0..2....0..2....2..1....0..1....0..1....0..2....0..1....0..2....1..0

..0..1....1..0....1..0....1..2....1..0....2..0....1..0....1..0....2..0....0..1

..2..1....0..1....0..1....2..1....0..1....0..2....0..1....0..1....0..2....2..2

CROSSREFS

Cf. A207149.

Sequence in context: A033980 A342903 A207149 * A244277 A248688 A291495

Adjacent sequences: A207139 A207140 A207141 * A207143 A207144 A207145

KEYWORD

nonn

AUTHOR

R. H. Hardin, Feb 15 2012

STATUS

approved

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Last modified January 28 07:13 EST 2023. Contains 359850 sequences. (Running on oeis4.)