A364486 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 vertex.

1, 1, 1, 2, 2, 5, 5, 13, 13, 32, 36, 85, 98, 226, 270, 610, 754, 1674, 2111, 4647, 5945, 13008, 16843, 36666, 47931, 103887, 136971, 295713, 392856, 845153, 1130268, 2424156, 3260969, 6975700, 9431977, 20130758, 27342941, 58243283, 79431140, 168900755, 231186046

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<6. The highest point of the polyomino on the vertical axis of symmetry must be a cell vertex.
             ________      ________              ________
   /\    /\  \  /\  /  /\  \  /\  /  /\  /\     /\  /\  /\
  /__\  /__\  \/__\/  /__\  \/__\/  /__\/__\   /__\/__\/__\
        \  /         /\  /\  \  /   \  /\  /
         \/         /__\/__\  \/     \/__\/
		

Links

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

Crossrefs

Cf. A030223, A364485, A364487.

Formula

a(n) = 2*A030223(n) - A364487(n), n odd.

a(n) = 2*A030223(n) - A364485(n/2) - A364487(n), n even.