login
A348402
Number of unoriented polyomino rings of length 2n with twofold rotational symmetry.
3
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
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
KEYWORD
nonn,more
AUTHOR
John Mason, Oct 18 2021
STATUS
approved