The Triangle Graph of order n has n rows with k vertices in row k. Each vertex is connected to the neighbors in the same row and up to two vertices in each of the neighboring rows. The Graph has A000217(n) vertices and 3*A000217(n-1) edges altogether.

For n = 4 the Triangle Graph of order 4 has 10 vertices and 18 edges. If vertices are numbered from left to right in each row and ascending with row numbers, the a(4) = 6 Hamiltonian cycles are (1,2,4,7,8,5,9,10,6,3), (1,2,4,7,8,9,10,6,5,3), (1,2,5,4,7,8,9,10,6,3), (1,3,5,6,10,9,8,7,4,2), (1,3,6,10,9,5,8,7,4,2), (1,3,6,10,9,8,7,4,5,2).