A208286 Number of n X 7 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

42, 1764, 14946, 70216, 239490, 665892, 1604862, 3478160, 6942474, 12974340, 22973082, 38883480, 63339874, 99833412, 152904150, 228359712, 333522218, 477505188, 671522130, 929228520, 1267098882, 1704840676, 2265846702

Offset

1,1

Comments

Column 7 of A208287.

Links

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

Formula

Empirical: a(n) = (61/180)*n^7 + (121/20)*n^6 + (1157/36)*n^5 + (425/12)*n^4 - (2923/90)*n^3 - (22/15)*n^2 + 2*n.

Conjectures from Colin Barker, Jun 29 2018: (Start)

G.f.: 2*x*(21 + 714*x + 1005*x^2 - 1156*x^3 + 203*x^4 + 86*x^5 - 19*x^6) / (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..0..1..1..1..0....1..0..1..1..0..1..1....1..0..1..1..1..0..0
..1..1..1..0..1..1..0....0..1..0..1..1..1..1....0..1..0..1..1..0..1
..1..1..1..1..1..1..0....1..0..1..1..0..1..1....0..1..1..1..1..0..1
..1..1..1..0..1..1..0....1..0..1..1..1..1..1....0..1..1..1..1..0..1

Crossrefs

Cf. A208287.

Sequence in context: A207953 A207862 A207812 * A208419 A208027 A207807

Adjacent sequences: A208283 A208284 A208285 * A208287 A208288 A208289

Keyword

nonn

Author

R. H. Hardin, Feb 25 2012

Status

approved