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

Author

Robert A. Russell, Jul 26 2023

Keywords

• nonn

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.

Examples

			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.
  ____   ____   ____________   ____      ____
  \  /  /\  /\  \  /\  /\  /  /\  /\    /\  /\
   \/  /__\/__\  \/__\/__\/  /__\/__\  /__\/__\
                             \  /\  /  \  /\  /
                              \/  \/    \/__\/
		

Links

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

Crossrefs

Cf. A030223, A364485, A364486.

Formula

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

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