A364487 Number of fixed triangular n-ominoes of the regular tiling with Schläfli symbol {3,6} that have a common axis of symmetry coincident with cell altitudes and the point of the polyomino farthest along that axis in a specified direction is a cell edge center.

1, 0, 1, 0, 2, 1, 5, 2, 13, 5, 36, 16, 96, 45, 262, 128, 720, 368, 1991, 1047, 5549, 2995, 15583, 8607, 44027, 24788, 125043, 71620, 356706, 207412, 1021318, 601719, 2933861, 1748874, 8452723, 5091776, 24417793, 14848210, 70706750, 43364962, 205193316, 126828277

Offset

1,5

Comments

This is one of three sequences used to calculate A030223, the number of achiral polyominoes for this tiling. Two fixed polyominoes are identical only if one is a translation of the other.

Links

Robert A. Russell, Table of n, a(n) for n = 1..60

Formula

a(n) = 2*A030223(n) - A364486(n), n odd.

a(n) = 2*A030223(n) - A364485(n/2) - A364486(n), n even.

Example

These are the n-ominoes for n<7. The highest point of the polyomino on the vertical axis of symmetry must be an edge center.
  ____   ____   ____________   ____      ____
  \  /  /\  /\  \  /\  /\  /  /\  /\    /\  /\
   \/  /__\/__\  \/__\/__\/  /__\/__\  /__\/__\
                             \  /\  /  \  /\  /
                              \/  \/    \/__\/

Crossrefs

Cf. A030223, A364485, A364486.

Sequence in context: A109191 A087123 A097131 * A192263 A109738 A258307

Adjacent sequences: A364484 A364485 A364486 * A364488 A364489 A364490

Keyword

nonn

Author

Robert A. Russell, Jul 26 2023

Status

approved