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%I #17 Jun 04 2021 14:44:49
%S 1,2,4,6,6,8,9,11,12,14,15,18,17,22,21,22,25,26,27,31,31,32,33,34,38,
%T 39,43,42,42,44,48,50,49,50,47,54,51,56,57,59,61,55,66,67,69,70,67,72,
%U 76,77,82,81,78,80,83,83,83,87,89,93,91,98,94,97,93,99,98
%N a(n) is the number of nodes of degree 3 or 4 that are at distance n from the origin in the graph of the Hofstetter-4fold tiling; a(0) = 1.
%C We build the Hofstetter-4fold tiling as follows:
%C - H_0 corresponds to a 2 X 2 square:
%C +---+---+
%C | |
%C + +
%C | |
%C +---+---+
%C O
%C - for any k >= 0, H_{k+1} is obtained by arranging 4 copies of H_k, rotated by 0, 90, 180, 270 degrees clockwise respectively, as follows:
%C +.......+
%C . 90.
%C +.......+ +.......+ ....+
%C . . .0 . . .
%C . . --> . ..... .
%C . . . . 180.
%C +.......+ +.......+.......+
%C O O .270 .
%C +.......+
%C - note that:
%C - the copy rotated by 0 degrees hides some squares on the copies rotated by 90 and 270 degrees,
%C - the copy rotated by 90 degrees hides some squares on the copy rotated by 180 degrees,
%C - the copy rotated by 180 degrees hides some squares on the copy rotated by 270 degrees,
%C - the Hofstetter-4fold tiling corresponds to the limit of H_k as k tends to infinity.
%H Rémy Sigrist, <a href="/A342597/b342597.txt">Table of n, a(n) for n = 0..5000</a>
%H Rémy Sigrist, <a href="/A342597/a342597.png">Illustration of initial terms</a>
%H Rémy Sigrist, <a href="/A342597/a342597_1.png">Colored representation of the nodes at distance <= 512 from the origin</a> (the color is a function of the distance)
%H Rémy Sigrist, <a href="/A342597/a342597.txt">C# program for A342597</a>
%H Tilings Encyclopedia, <a href="https://tilings.math.uni-bielefeld.de/substitution/hofstetter-4fd-plain/">Hofstetter-4fold (plain)</a>
%H <a href="/index/Con#coordination_sequences">Index entries for coordination sequences</a>
%e See illustration in Links section.
%o (C#) See Links section.
%Y Cf. A342425, A342577.
%K nonn
%O 0,2
%A _Rémy Sigrist_, Mar 16 2021
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