A350296 - OEIS

%I #12 Dec 25 2024 00:51:25

%S 0,1,3,7,13,20,28,40,52,66,82,99,117,140,164,189,215,243,273,304,336,

%T 376,414,454

%N Minimum number of 1's in an n X n binary matrix with no zero 2 X 2 submatrix.

%F a(n) = A347472(n) + 1 = n^2 - A001197(n) + 1 = n^2 - A072567(n).

%F a(n) >= A152125(n).

%e Solutions for a(3)=3, a(4)=7, a(5)=13, a(6)=20:

%e   . . x    . . . x    . . . . x    . . . x x x

%e   . x .    . x x .    . x x x .    . x x . . x

%e   x . .    x . x .    x . x x .    x . x . x .

%e            x x . .    x x . x .    x x . x . .

%e                       x x x . .    . x x x x .

%e                                    x . x x . x

%Y Column 2 of A339635.

%Y Cf. A001197, A072567, A152125, A227133, A347472.

%K nonn,more

%O 1,3

%A _Andrew Howroyd_, Dec 23 2021

%E a(22)-a(24) computed from A001197, added by _Max Alekseyev_, Feb 08 2022