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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 0

%I

%S 1,4,9,12,23,36,49,64,73,100,115,144,169,192,225,248,287,324,345,400,

%T 441,484,515,572,625,676,729,784,831,880,961,1004,1073,1152,1219,1296,

%U 1369,1444,1489,1600,1679,1764,1849,1932,2025,2116,2179,2304,2393,2492

%N 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

%C Diagonal of A220196.

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

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

%e Some solutions for n=3

%e ..1..1..0....0..1..1....0..0..0....1..1..1....0..1..0....1..0..0....0..0..1

%e ..1..0..1....0..0..0....0..0..1....1..1..0....0..0..0....0..0..1....1..0..1

%e ..1..0..0....1..0..0....1..0..0....0..1..0....1..1..1....0..0..0....1..1..0

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

%Y Cf. A159257, A220196.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 07 2012

%E More terms from _Vincenzo Librandi_, Feb 10 2017

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Last modified October 23 22:10 EDT 2019. Contains 328373 sequences. (Running on oeis4.)