A188822 Number of n X 7 binary arrays without the pattern 0 1 diagonally or antidiagonally.

128, 1156, 3888, 8836, 15776, 24964, 36000, 49284, 64416, 81796, 101024, 122500, 145824, 171396, 198816, 228484, 260000, 293764, 329376, 367236, 406944, 448900, 492704, 538756, 586656, 636804, 688800, 743044, 799136, 857476, 917664, 980100

Offset

1,1

Comments

Column 7 of A188824.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4) for n>7.

Conjectures from Colin Barker, Apr 30 2018: (Start)

G.f.: 4*x*(32 + 225*x + 394*x^2 + 329*x^3 + 72*x^4 + 8*x^5 - 36*x^6) / ((1 - x)^3*(1 + x)).

a(n) = 2*(578 - 1088*n + 512*n^2) for n>3 and even.

a(n) = 2*(528 - 1088*n + 512*n^2) for n>3 and odd.

(End)

Example

Some solutions for 3 X 7:
..1..1..1..0..1..1..1....1..1..1..1..1..0..1....1..1..1..1..1..1..1
..1..1..0..0..0..0..1....1..1..0..1..0..1..0....1..0..1..0..0..1..0
..0..0..0..0..0..0..0....1..0..1..0..0..0..0....0..1..0..0..0..0..0

Crossrefs

Cf. A188824.

Sequence in context: A221599 A134630 A133061 * A181211 A221071 A070055

Adjacent sequences: A188819 A188820 A188821 * A188823 A188824 A188825

Keyword

nonn

Author

R. H. Hardin, Apr 11 2011

Status

approved