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

1,4

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) - A364487(n), n odd.

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

Example

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.
             ________      ________              ________
   /\    /\  \  /\  /  /\  \  /\  /  /\  /\     /\  /\  /\
  /__\  /__\  \/__\/  /__\  \/__\/  /__\/__\   /__\/__\/__\
        \  /         /\  /\  \  /   \  /\  /
         \/         /__\/__\  \/     \/__\/

Crossrefs

Cf. A030223, A364485, A364487.

Sequence in context: A122205 A368923 A338762 * A178115 A094967 A322111

Adjacent sequences: A364483 A364484 A364485 * A364487 A364488 A364489

Keyword

nonn

Author

Robert A. Russell, Jul 26 2023

Status

approved