A261212 Maximum number of 1's in an fully symmetrical n X n binary matrix with no three 1's adjacent in a line along a row, column or diagonally.

1, 4, 4, 8, 16, 20, 25, 36, 41, 48, 64, 72, 81, 100, 109, 120, 144, 156, 173, 196, 213, 228, 256, 272, 300, 324, 349, 368, 401, 424, 457, 484

Offset

1,2

Comments

Fully symmetrical refers to the four symmetry axes: horizontal, vertical and two diagonal.

Note that a(3k+2) = 4*(1+k)^2, for k=0,...,8, but a(29) = 401.

Links

Table of n, a(n) for n=1..32.

Giovanni Resta, Illustration of a(6)-a(30)

Formula

a(n) <= A181018(n).

a(3k+2) >= 4*(k+1)^2.

Example

For n=4, the matrix is
0 1 0
1 0 1
0 1 0
For n=6, the matrix is
1 1 0 0 1 1
1 0 1 1 0 1
0 1 0 0 1 0
0 1 0 0 1 0
1 0 1 1 0 1
1 1 0 0 1 1

Crossrefs

Cf. A181018.

Sequence in context: A190100 A244421 A030168 * A112435 A232508 A028610

Adjacent sequences: A261209 A261210 A261211 * A261213 A261214 A261215

Keyword

nonn

Author

V.J. Pohjola and Giovanni Resta, Aug 12 2015

Status

approved