A349329 Number of polyominoes with 2n cells and exactly one line of reflection symmetry, where that one line is parallel to the grid and passes through the corner of at least one square.

0, 0, 2, 7, 28, 100, 368, 1335, 4912, 18125, 67477, 252573, 951363, 3601113, 13695150, 52291510, 200389661, 770391542, 2970337861, 11482318605, 44491635790, 172766013959, 672185703574, 2619993338628

Offset: 1

Author

John Mason, Nov 15 2021

Keywords

• nonn

Examples

			a(3)=2 because of hexominoes:
  OO   and   O
  O          OO
  O          OO
  OO         O
		

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, A349328.

Formula

a(n) = A006746(2n) - A349328(2n).

a(n) = 2*(A006747(n) + A006748(n)) + A144553(n) + A056878(n) + A006746(n) + 4*A006749(n). - corrected by John Mason, Feb 26 2023

Extensions

Name corrected by John Mason, Feb 01 2022