A234006 Free polyominoes with 2n squares, having reflectional symmetry on axis that coincides with edges.

1, 2, 4, 11, 35, 114, 392, 1381, 4998, 18292, 67791, 253182, 952527, 3603389, 13699516, 52300071, 200406183, 770424072, 2970400815, 11482442855, 44491876993, 172766491178, 672186631950, 2619995178793, 10228902801505, 39996341268584, 156612023001490, 614044347934591

Offset: 1

Author

John Mason, Dec 18 2013

Keywords

• nonn

Comments

The number of free polyominoes of size 2n that have reflectional symmetry on a horizontal or vertical axis that coincides with the edges of some of the squares. The sequence is defined for 2n rather than n as odd-sized polyominoes cannot have the required symmetry.

Links

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

Crossrefs

Cf. A000105, A001168, A001933, A151525, A182645, A234007, A234008, A234009, A234010, A349329, A346799, A346800, A351191.

Programs

Mathematica

A151525 = Cases[Import["https://oeis.org/A151525/b151525.txt", "Table"], {, }][[All, 2]];
A182645 = Cases[Import["https://oeis.org/A182645/b182645.txt", "Table"], {, }][[All, 2]];
A001168 = Cases[Import["https://oeis.org/A001168/b001168.txt", "Table"], {, }][[All, 2]];
a[n_] := If[OddQ[n], A151525[[n]], A151525[[n]] + A182645[[n/2]] - A001168[[n/2]]];
Array[a, 28] (* Jean-François Alcover, Sep 10 2019, after Andrew Howroyd *)

Formula

a(2*n+1) = A151525(2*n+1), a(2*n) = A151525(2*n) + A182645(n) - A001168(n). - Andrew Howroyd, Dec 05 2018

If n odd, a(n) = A349329(n) + A346799(n), otherwise a(n) = A349329(n) + A346799(n) + A346800(n/2) + A351191(n/2). - John Mason, Mar 15 2023

Extensions

a(12)-a(28) from Andrew Howroyd, Dec 05 2018