A349328 Number of polyominoes with n cells and exactly one line of reflection symmetry, where that one line is parallel to the grid and passes through the center of at least one square.

0, 0, 0, 1, 2, 4, 9, 16, 38, 62, 147, 241, 564, 926, 2148, 3561, 8195, 13700, 31349, 52858, 120357, 204444, 463712, 792986, 1792582, 3083469, 6950579, 12018394, 27023509, 46943409, 105320716, 183715445, 411364068, 720236762, 1609836928, 2828102115

Offset: 1

Author

John Mason, Nov 15 2021

Keywords

• nonn

Examples

			a(4) is 1 because of the tetromino:
   O
  OOO
		

Links

• John Mason, Table of n, a(n) for n = 1..50

Crossrefs

Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554, A349329.

Formula

For odd n, a(n) = A006746(n).

For even n, a(n) = A006746(n) - A349329(n/2).