A392392 Number of free polyquarcs with n cells.

1, 2, 4, 13, 38, 141, 521, 2064, 8155, 33111, 135271, 559215, 2324502, 9726175, 40887925, 172669360, 731895102, 3112855720

Offset

1,2

Comments

The cells of a polyquarc are quarter circular arcs of equal radii. Two cells are connected if one end from each meet along a common tangent line head to head, so that no cusp is created at the junction. However, such cusps are allowed to exist provided that the polyquarc is connected via non-cusp junctions.

Cells can be represented as integer points in the plane, with the neighbors of (x,y) being (x,y-s), (x-r,y), (x+r,y-s), (x-r,y+s), where r = (-1)^(x mod 2) and s = (-1)^(y mod 2).

Links

Table of n, a(n) for n=1..18.

Pontus von Brömssen, Illustration for n=1..5.

Crossrefs

Cf. A187210, A187220, A392389, A392393 (one-sided), A392394 (fixed), A393000.

Sequence in context: A394068 A148253 A385272 * A148254 A163137 A093630

Adjacent sequences: A392389 A392390 A392391 * A392393 A392394 A392395

Keyword

nonn,more

Author

Pontus von Brömssen, Jan 15 2026

Extensions

a(15)-a(18) from Christian Sievers, Jan 16 2026

Status

approved