A220195 Sum of neighbor maps: log base 2 of the number of n X n binary arrays indicating the locations of corresponding elements equal to the sum mod 2 of their horizontal and vertical neighbors in a random 0..1 n X n array.

1, 4, 9, 12, 23, 36, 49, 64, 73, 100, 115, 144, 169, 192, 225, 248, 287, 324, 345, 400, 441, 484, 515, 572, 625, 676, 729, 784, 831, 880, 961, 1004, 1073, 1152, 1219, 1296, 1369, 1444, 1489, 1600, 1679, 1764, 1849, 1932, 2025, 2116, 2179, 2304, 2393, 2492

Offset: 1

Author

R. H. Hardin, Dec 07 2012

Keywords

• nonn

Comments

Diagonal of A220196.

Also, equals n^2 - A159257(n).

The entries describe the rank of the Lights Out problem of size n (see A159257).

Examples

			Some solutions for n=3
..1..1..0....0..1..1....0..0..0....1..1..1....0..1..0....1..0..0....0..0..1
..1..0..1....0..0..0....0..0..1....1..1..0....0..0..0....0..0..1....1..0..1
..1..0..0....1..0..0....1..0..0....0..1..0....1..1..1....0..0..0....1..1..0
		

Crossrefs

Cf. A159257, A220196.

Programs

Mathematica

Table[n^2 - (First[Dimensions[NullSpace[AdjacencyMatrix[GridGraph[{n, n}]] + IdentityMatrix[n*n], Modulus->2]]]), {n, 1, 40}] (* Vincenzo Librandi, Feb 10 2017 *)

Extensions

More terms from Vincenzo Librandi, Feb 10 2017