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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.
4
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
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
KEYWORD
nonn
AUTHOR
Robert A. Russell, Jul 26 2023
STATUS
approved