A350296 Minimum number of 1's in an n X n binary matrix with no zero 2 X 2 submatrix.

0, 1, 3, 7, 13, 20, 28, 40, 52, 66, 82, 99, 117, 140, 164, 189, 215, 243, 273, 304, 336, 376, 414, 454

Offset

1,3

Links

Table of n, a(n) for n=1..24.

Formula

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

a(n) >= A152125(n).

Example

Solutions for a(3)=3, a(4)=7, a(5)=13), a(6)=20:
  . . x    . . . x    . . . . x    . . . x x x
  . x .    . x x .    . x x x .    . x x . . x
  x . .    x . x .    x . x x .    x . x . x .
           x x . .    x x . x .    x x . x . .
                      x x x . .    . x x x x .
                                   x . x x . x

Crossrefs

Column 2 of A339635.

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

Sequence in context: A294398 A330707 A033551 * A022777 A033154 A076950

Adjacent sequences: A350293 A350294 A350295 * A350297 A350298 A350299

Keyword

nonn,more

Author

Andrew Howroyd, Dec 23 2021

Extensions

a(22)-a(24) computed from A001197, added by Max Alekseyev, Feb 08 2022

Status

approved