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A323183 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.

%I A323183 #15 Nov 11 2019 00:31:23
%S A323183 1,4,20,39,55,71,91,107,129,147,165,181,197,217,233,253,269,289,305,
%T A323183 325,341,361,377,399,417,435,453,471,489,507,525,543,559,575,595,611,
%U A323183 631,647,667,683,703,719,739,755,775,791,811,827,847,863,883,899,919,935
%N A323183 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 A323183 The variant relative to the central node appears to match A019557.
%H A323183 Rémy Sigrist, <a href="/A323183/a323183.png">Illustration of initial terms</a>
%H A323183 Rémy Sigrist, <a href="/A323183/a323183.cs.txt">C# program for A323183</a>
%H A323183 Tilings Encyclopedia, <a href="http://tilings.math.uni-bielefeld.de/substitution/equithirds/">Equithirds</a>
%H A323183 <a href="/index/Con#coordination_sequences">Index entries for sequences related to coordination sequences</a>
%o A323183 (C#) See Links section.
%Y A323183 Cf. A019557, A323187 (partial sums).
%K A323183 nonn
%O A323183 0,2
%A A323183 _Rémy Sigrist_, Jan 06 2019