A208141 Number of n X 7 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

20, 400, 3000, 14000, 49000, 141120, 352800, 792000, 1633500, 3146000, 5725720, 9937200, 16562000, 26656000, 41616000, 63256320, 93896100, 136458000, 194579000, 272734000, 376372920, 512072000, 687700000, 912600000, 1197787500

Offset

1,1

Comments

Column 7 of A208142.

Links

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

Formula

Empirical: a(n) = (5/36)*n^7 + (5/4)*n^6 + (155/36)*n^5 + (85/12)*n^4 + (50/9)*n^3 + (5/3)*n^2.

Conjectures from Colin Barker, Jun 28 2018: (Start)

G.f.: 20*x*(1 + 12*x + 18*x^2 + 4*x^3) / (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:
..0..1..0..1..0..0..0....1..1..0..1..0..1..0....0..0..0..0..0..0..0
..1..0..0..0..0..0..0....1..1..0..1..0..1..0....1..1..1..0..0..0..0
..0..0..0..0..0..0..0....0..1..0..0..0..0..0....0..0..0..0..0..0..0
..0..0..0..0..0..0..0....0..1..0..0..0..0..0....0..0..0..0..0..0..0

Crossrefs

Cf. A208142.

Sequence in context: A207127 A207948 A206938 * A188603 A188610 A188847

Adjacent sequences: A208138 A208139 A208140 * A208142 A208143 A208144

Keyword

nonn

Author

R. H. Hardin, Feb 23 2012

Status

approved