A188501 - OEIS

A188501

Number of n X 2 binary arrays without the pattern 0 1 0 diagonally, vertically or horizontally.

4, 16, 49, 144, 441, 1369, 4225, 12996, 40000, 123201, 379456, 1168561, 3598609, 11082241, 34128964, 105103504, 323676081, 996791184, 3069714025, 9453478441, 29112890625, 89655929476, 276104007936, 850288696321, 2618545348864

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OFFSET

1,1

COMMENTS

Column 2 of A188508.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200

FORMULA

Empirical: a(n)=3*a(n-1)-a(n-2)+3*a(n-3)+3*a(n-4)-a(n-5)-a(n-6).

Empirical g.f.: x*(4 + 4*x + 5*x^2 + x^3 - 2*x^4 - x^5) / ((1 - x + 2*x^2 - x^3)*(1 - 2*x - 3*x^2 - x^3)). - Colin Barker, Feb 18 2018

EXAMPLE

Some solutions for 3 X 2:

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

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

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

CROSSREFS

Sequence in context: A227266 A114185 A188516 * A283692 A173712 A085697

Adjacent sequences: A188498 A188499 A188500 * A188502 A188503 A188504

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 02 2011

STATUS

approved