A348402 Number of unoriented polyomino rings of length 2n with twofold rotational symmetry.

0, 1, 0, 1, 1, 3, 3, 9, 13, 35, 59, 147, 280, 669, 1347, 3142, 6545, 15110, 32057, 73625, 158056, 362280, 783800, 1795134, 3906573, 8946154, 19558340

Offset

1,6

Comments

This sequence and its chiral and achiral versions correspond to Robert A. Russell's similar sequences for rings of fourfold rotational symmetry. The sequence does not count the mononimo or domino, referred to by Redelmeier as degenerate rings, as they are not in fact rings.

The sequence refers to rings with at least twofold (180-degree) rotational symmetry, and so includes those with (i) fourfold (90-degree) rotational symmetry, and (ii) all symmetries. - John Mason, Jan 19 2023

Links

Table of n, a(n) for n=1..27.

D. H. Redelmeier, Counting polyominoes: yet another attack, Discrete Math., 36 (1981), 191-203.

Formula

a(n) = A348403(n) + A348404(n).

Example

a(2)=1 because of:
  OO
  OO
a(4)=1 because of:
  OOO
  O.O
  OOO
a(5)=1 because of:
  OOOO
  O..O
  OOOO

Crossrefs

Cf. A348403 (chiral), A348404 (achiral), A324407 (unoriented with fourfold rotational symmetry), A324408 (chiral with fourfold rotational symmetry), A324409 (achiral with fourfold rotational symmetry).

Sequence in context: A183811 A303640 A091328 * A138383 A052436 A243790

Adjacent sequences: A348399 A348400 A348401 * A348403 A348404 A348405

Keyword

nonn,more

Author

John Mason, Oct 18 2021

Status

approved