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A266513 Number of undirected cycles in a triangular grid graph, n vertices on each side.

%I A266513 #28 Feb 16 2025 08:33:28
%S A266513 0,1,11,110,2402,128967,16767653,5436906668,4406952731948,
%T A266513 8819634719356421,43329348004927734247,522235268182347360718818,
%U A266513 15436131339319739257518081878,1117847654274955574635482276231683,198163274851163063009517020867737770265
%N A266513 Number of undirected cycles in a triangular grid graph, n vertices on each side.
%H A266513 Ed Wynn, <a href="/A266513/b266513.txt">Table of n, a(n) for n = 1..17</a>
%H A266513 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A266513 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TriangularGridGraph.html">Triangular Grid Graph</a>
%e A266513 Of the 11 cycles in the triangular grid with 3 vertices per side, 4 have length 3, 3 have length 4, 3 have length 5 and 1 has length 6.
%e A266513 4 basic cycle shapes on a(3):
%e A266513                                       o
%e A266513                                      / \
%e A266513         o       o---o    o---o      o   o
%e A266513        / \     /   /    /     \    /     \
%e A266513       o---o   o---o    o---o---o  o---o---o
%o A266513 (Python)
%o A266513 # Using graphillion
%o A266513 from graphillion import GraphSet
%o A266513 def make_n_triangular_grid_graph(n):
%o A266513     s = 1
%o A266513     grids = []
%o A266513     for i in range(n + 1, 1, -1):
%o A266513         for j in range(i - 1):
%o A266513             a, b, c = s + j, s + j + 1, s + i + j
%o A266513             grids.extend([(a, b), (a, c), (b, c)])
%o A266513         s += i
%o A266513     return grids
%o A266513 def A266513(n):
%o A266513     if n == 1: return 0
%o A266513     universe = make_n_triangular_grid_graph(n - 1)
%o A266513     GraphSet.set_universe(universe)
%o A266513     cycles = GraphSet.cycles()
%o A266513     return cycles.len()
%o A266513 print([A266513(n) for n in range(1, 12)])  # _Seiichi Manyama_, Nov 30 2020
%Y A266513 Cf. A112676, A112675, A140517, A269869.
%K A266513 nonn
%O A266513 1,3
%A A266513 _Andrew Howroyd_, Apr 06 2016