A183271 Half the number of n X n X n triangular binary arrays with the number of 0-0 adjacencies equal to the number of 1-1 adjacencies.

1, 0, 0, 65, 1578, 0, 0, 1875535329, 839252581538, 0, 0, 5227844810759073967200, 39228698077486633860579435, 0, 0, 1102249786277252805957700361396650437576, 135380785027014267422923708062639569342712090, 0, 0

Offset

1,4

Comments

a(n)=0 for n mod 4 = 2 or 3 because the number of edges is odd and flipping a 0 to a 1 changes the relative counts by an even number.

Links

R. H. Hardin, Table of n, a(n) for n = 1..59

Example

Some solutions for 4 X 4 X 4 with a(1,1)=0 and an equal number of 0-0 and 1-1 adjacencies:
.....0........0........0........0........0........0........0........0
....1.0......1.0......0.0......1.0......1.1......1.0......0.1......1.1
...1.0.0....1.0.0....1.0.1....1.0.1....0.1.1....0.0.1....1.0.1....0.0.0
..1.1.1.0..0.1.1.1..0.1.1.1..1.1.0.0..0.0.0.0..0.1.1.1..0.1.0.1..1.1.1.0

Crossrefs

Sequence in context: A086029 A221038 A221501 * A197088 A031604 A002502

Adjacent sequences: A183268 A183269 A183270 * A183272 A183273 A183274

Keyword

nonn

Author

R. H. Hardin, Jan 03 2011

Status

approved