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

1,3

Links

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

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

Example

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

Crossrefs

Sequences classifying polyominoes by symmetry group: A000105, A006746, A006747, A006748, A006749, A056877, A056878, A142886, A144553, A144554, A349328.

Sequence in context: A123363 A102961 A155581 * A048504 A092465 A099488

Adjacent sequences: A349326 A349327 A349328 * A349330 A349331 A349332

Keyword

nonn

Author

John Mason, Nov 15 2021

Extensions

Name corrected by John Mason, Feb 01 2022

Status

approved