A378921 Number of binary n X n matrices that do not possess both horizontal and vertical symmetry.

0, 0, 14, 496, 65520, 33553920, 68719476224, 562949953355776, 18446744073709486080, 2417851639229258315857920, 1267650600228229401496669650944, 2658455991569831745807614051841212416, 22300745198530623141535718272648292786503680, 748288838313422294120286634350736905500887508582400

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Formula

a(n) = 2^(n^2) - 2^(ceiling(n/2)^2).

a(n) = A002416(n) - A002416(A110654(n)).

Example

For a 2 x 2 matrix we have 14 such matrices:
  _x  __  x_  __  _x  xx  _x
  __, _x, __, x_, x_, __, _x,
  x_  xx  _x  xx  x_  __  x_
  xx, x_, xx, _x, _x, xx, x_

Prog

(Python)
def a(n): return (1 << (n * n)) - (1 << (((n + 1) // 2) * ((n + 1) // 2)))

Crossrefs

Cf. A002416, A110654.

Sequence in context: A240411 A024299 A190999 * A320288 A344114 A233014

Adjacent sequences: A378918 A378919 A378920 * A378922 A378923 A378924

Keyword

nonn

Author

Jwalin Bhatt, Dec 11 2024

Status

approved