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

1,2

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).

Links

Table of n, a(n) for n=1..50.

Example

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

Mathematica

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

Crossrefs

Cf. A159257, A220196.

Sequence in context: A186130 A051233 A124623 * A221355 A197681 A197624

Adjacent sequences: A220192 A220193 A220194 * A220196 A220197 A220198

Keyword

nonn

Author

R. H. Hardin, Dec 07 2012

Extensions

More terms from Vincenzo Librandi, Feb 10 2017

Status

approved