A207304 Number of n X 7 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

28, 784, 4344, 14446, 36868, 79802, 154228, 274288, 457660, 725932, 1104976, 1625322, 2322532, 3237574, 4417196, 5914300, 7788316, 10105576, 12939688, 16371910, 20491524, 25396210, 31192420, 37995752, 45931324, 55134148, 65749504

Offset

1,1

Comments

Column 7 of A207305.

Links

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

Formula

Empirical: a(n) = (187/60)*n^5 + (153/4)*n^4 + (455/12)*n^3 - (249/4)*n^2 + (209/30)*n + 4.

Conjectures from Colin Barker, Jun 22 2018: (Start)

G.f.: 2*x*(14 + 308*x + 30*x^2 - 209*x^3 + 46*x^4 - 2*x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

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

Crossrefs

Cf. A207305.

Sequence in context: A207168 A208012 A207789 * A207917 A208163 A207959

Adjacent sequences: A207301 A207302 A207303 * A207305 A207306 A207307

Keyword

nonn

Author

R. H. Hardin, Feb 16 2012

Status

approved