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Consider the family of configurations E where E(0) consists of a single equilateral triangle, and for any k >= 0, E(k+1) is obtained by applying the Equithirds substitution to E(k). For k >= 5, the central node of E(k) has 6 equivalent tetravalent neighbors; let t(k) be the coordination sequence for one of those tetravalent nodes. This sequence is the limit of t(k) as k goes to infinity.
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%I #15 Nov 11 2019 00:31:23

%S 1,4,20,39,55,71,91,107,129,147,165,181,197,217,233,253,269,289,305,

%T 325,341,361,377,399,417,435,453,471,489,507,525,543,559,575,595,611,

%U 631,647,667,683,703,719,739,755,775,791,811,827,847,863,883,899,919,935

%N Consider the family of configurations E where E(0) consists of a single equilateral triangle, and for any k >= 0, E(k+1) is obtained by applying the Equithirds substitution to E(k). For k >= 5, the central node of E(k) has 6 equivalent tetravalent neighbors; let t(k) be the coordination sequence for one of those tetravalent nodes. This sequence is the limit of t(k) as k goes to infinity.

%C The variant relative to the central node appears to match A019557.

%H Rémy Sigrist, <a href="/A323183/a323183.png">Illustration of initial terms</a>

%H Rémy Sigrist, <a href="/A323183/a323183.cs.txt">C# program for A323183</a>

%H Tilings Encyclopedia, <a href="http://tilings.math.uni-bielefeld.de/substitution/equithirds/">Equithirds</a>

%H <a href="/index/Con#coordination_sequences">Index entries for sequences related to coordination sequences</a>

%o (C#) See Links section.

%Y Cf. A019557, A323187 (partial sums).

%K nonn

%O 0,2

%A _Rémy Sigrist_, Jan 06 2019