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A286756 Irregular triangle T(n,k) for 0 <= k < 5n/2: T(n,k) = number of vertices of the cube-connected cycle graph of order n that are at a distance k from a designated vertex.

%I A286756 #13 Feb 16 2025 08:33:45
%S A286756 1,1,1,2,2,2,1,1,3,4,6,6,3,1,1,3,5,8,11,13,13,8,2,0,1,3,6,10,16,24,31,
%T A286756 32,23,11,3,0,1,3,6,11,18,29,43,58,72,71,47,19,5,1,0,1,3,6,12,20,34,
%U A286756 55,83,120,154,162,131,77,29,7,2,0
%N A286756 Irregular triangle T(n,k) for 0 <= k < 5n/2: T(n,k) = number of vertices of the cube-connected cycle graph of order n that are at a distance k from a designated vertex.
%C A286756 The cube-connected cycle graph of order n is a vertex transitive graph with n*2^n vertices and degree 3.
%C A286756 The radius of the graph is floor(5n/2)-1 for n<=3 and floor(5n/2)-2 for n>3.
%H A286756 Andrew Howroyd, <a href="/A286756/b286756.txt">Table of n, a(n) for n = 1..744</a>
%H A286756 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Cube-ConnectedCycleGraph.html">Cube-Connected Cycle Graph</a>
%e A286756 Triangle starts:
%e A286756 1, 1
%e A286756 1, 2, 2, 2, 1
%e A286756 1, 3, 4, 6, 6, 3, 1
%e A286756 1, 3, 5, 8,  11, 13, 13, 8, 2, 0
%e A286756 1, 3, 6, 10, 16, 24, 31, 32, 23, 11, 3, 0
%e A286756 1, 3, 6, 11, 18, 29, 43, 58, 72, 71, 47, 19, 5, 1, 0
%e A286756 1, 3, 6, 12, 20, 34, 55, 83, 120, 154, 162, 131, 77, 29, 7, 2, 0
%e A286756 ...
%e A286756 The order 3 graph has 24 vertices. For k=1 to 6 there are 3, 4, 6, 6, 3, 1 vertices at a distance k from any vertex in the graph.
%Y A286756 Row sums are A036289.
%Y A286756 Cf. A192191.
%K A286756 nonn,tabf
%O A286756 1,4
%A A286756 _Andrew Howroyd_, May 13 2017