A228277 Number of n X n binary arrays with top left value 1 and no two ones adjacent horizontally, vertically or nw-se diagonally.

1, 1, 13, 133, 3631, 172082, 16566199, 3057290265, 1105411581741, 776531523355217, 1063228770141145384, 2834013489992345694498, 14712337761578682394367473, 148727865257442275211424889367

Offset

1,3

Comments

Main diagonal of A228285.

Links

R. H. Hardin, Table of n, a(n) for n = 1..25

Formula

No known recurrence.

Example

The thirteen solutions for n=3 correspond to the thirteen possible values of 5-bit numbers with no two adjacent bits equal to 1, namely, the matrices
( 1 0 a )
( 0 0 b )
( e d c ) ; with abcde = A014417(0,...,12) = 0, 1, 10, 100, 101, 1000, 1001, 1010, 10000, 10001, 10010, 10100, 10101 (leading zeros omitted). - M. F. Hasler, Apr 27 2014
Some solutions for n=4:
.1..0..0..1.  .1..0..0..0.  .1..0..0..0.  .1..0..0..0.  .1..0..0..0
.0..0..0..0.  .0..0..0..1.  .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..0.  .0..0..0..1
.1..0..0..1.  .0..1..0..1.  .0..1..0..1.  .0..1..0..0.  .0..0..1..0
The last example shows that sw-ne (= anti)diagonally adjacent "1"s are allowed. See A228476, A228506 and A228390 for other variants.

Crossrefs

Cf. A228277-A228285.

See also the variants A228390, A228476, A228506, etc.

Sequence in context: A097166 A073556 A154999 * A221153 A297335 A262572

Adjacent sequences: A228274 A228275 A228276 * A228278 A228279 A228280

Keyword

nonn

Author

R. H. Hardin, Aug 19 2013

Status

approved