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%I #10 Aug 06 2023 11:55:24
%S 1,0,1,0,2,1,5,2,13,5,36,16,96,45,262,128,720,368,1991,1047,5549,2995,
%T 15583,8607,44027,24788,125043,71620,356706,207412,1021318,601719,
%U 2933861,1748874,8452723,5091776,24417793,14848210,70706750,43364962,205193316,126828277
%N 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.
%C 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.
%H Robert A. Russell, <a href="/A364487/b364487.txt">Table of n, a(n) for n = 1..60</a>
%F a(n) = 2*A030223(n) - A364486(n), n odd.
%F a(n) = 2*A030223(n) - A364485(n/2) - A364486(n), n even.
%e 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.
%e ____ ____ ____________ ____ ____
%e \ / /\ /\ \ /\ /\ / /\ /\ /\ /\
%e \/ /__\/__\ \/__\/__\/ /__\/__\ /__\/__\
%e \ /\ / \ /\ /
%e \/ \/ \/__\/
%Y Cf. A030223, A364485, A364486.
%K nonn
%O 1,5
%A _Robert A. Russell_, Jul 26 2023
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