cp's OEIS Frontend

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.

%I A364486 #12 Aug 06 2023 11:55:29
%S A364486 1,1,1,2,2,5,5,13,13,32,36,85,98,226,270,610,754,1674,2111,4647,5945,
%T A364486 13008,16843,36666,47931,103887,136971,295713,392856,845153,1130268,
%U A364486 2424156,3260969,6975700,9431977,20130758,27342941,58243283,79431140,168900755,231186046
%N 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.
%C A364486 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 A364486 Robert A. Russell, <a href="/A364486/b364486.txt">Table of n, a(n) for n = 1..60</a>
%F A364486 a(n) = 2*A030223(n) - A364487(n), n odd.
%F A364486 a(n) = 2*A030223(n) - A364485(n/2) - A364487(n), n even.
%e A364486 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.
%e A364486              ________      ________              ________
%e A364486    /\    /\  \  /\  /  /\  \  /\  /  /\  /\     /\  /\  /\
%e A364486   /__\  /__\  \/__\/  /__\  \/__\/  /__\/__\   /__\/__\/__\
%e A364486         \  /         /\  /\  \  /   \  /\  /
%e A364486          \/         /__\/__\  \/     \/__\/
%Y A364486 Cf. A030223, A364485, A364487.
%K A364486 nonn
%O A364486 1,4
%A A364486 _Robert A. Russell_, Jul 26 2023