A207110 Number of n X 7 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically

25, 625, 3399, 11511, 30415, 68737, 139341, 260597, 457869, 765241, 1227499, 1902387, 2863155, 4201417, 6030337, 8488161, 11742113, 15992673, 21478255, 28480303, 37328823, 48408369, 62164501, 79110733, 99835989, 125012585

Offset

1,1

Comments

Column 7 of A207111.

Links

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

Formula

Empirical: a(n) = (1/280)*n^7 + (7/45)*n^6 + (47/15)*n^5 + (206/9)*n^4 + (4111/120)*n^3 - (1037/45)*n^2 - (4493/210)*n + 9.

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

G.f.: x*(25 + 425*x - 901*x^2 + 419*x^3 + 249*x^4 - 269*x^5 + 79*x^6 - 9*x^7) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

Example

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

Crossrefs

Cf. A207111.

Sequence in context: A207367 A207499 A207241 * A207466 A207701 A207906

Adjacent sequences: A207107 A207108 A207109 * A207111 A207112 A207113

Keyword

nonn

Author

R. H. Hardin, Feb 15 2012

Status

approved