A261212 - OEIS

%I #22 Aug 19 2015 15:20:17

%S 1,4,4,8,16,20,25,36,41,48,64,72,81,100,109,120,144,156,173,196,213,

%T 228,256,272,300,324,349,368,401,424,457,484

%N 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.

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

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

%H Giovanni Resta, <a href="/A261212/a261212.pdf">Illustration of a(6)-a(30)</a>

%F a(n) <= A181018(n).

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

%e For n=4, the matrix is

%e 0 1 0

%e 1 0 1

%e 0 1 0

%e For n=6, the matrix is

%e 1 1 0 0 1 1

%e 1 0 1 1 0 1

%e 0 1 0 0 1 0

%e 0 1 0 0 1 0

%e 1 0 1 1 0 1

%e 1 1 0 0 1 1

%Y Cf. A181018.

%K nonn

%O 1,2

%A _V.J. Pohjola_ and _Giovanni Resta_, Aug 12 2015