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

0, 1, 11, 110, 2402, 128967, 16767653, 5436906668, 4406952731948, 8819634719356421, 43329348004927734247, 522235268182347360718818, 15436131339319739257518081878, 1117847654274955574635482276231683, 198163274851163063009517020867737770265

Offset: 1

Author

Andrew Howroyd, Apr 06 2016

Keywords

• nonn

Examples

			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.
4 basic cycle shapes on a(3):
                                      o
                                     / \
        o       o---o    o---o      o   o
       / \     /   /    /     \    /     \
      o---o   o---o    o---o---o  o---o---o
		

Links

• Ed Wynn, Table of n, a(n) for n = 1..17
• Eric Weisstein's World of Mathematics, Graph Cycle
• Eric Weisstein's World of Mathematics, Triangular Grid Graph

Crossrefs

Cf. A112676, A112675, A140517, A269869.

Programs

Python

# Using graphillion
from graphillion import GraphSet
def make_n_triangular_grid_graph(n):
    s = 1
    grids = []
    for i in range(n + 1, 1, -1):
        for j in range(i - 1):
            a, b, c = s + j, s + j + 1, s + i + j
            grids.extend([(a, b), (a, c), (b, c)])
        s += i
    return grids
def A266513(n):
    if n == 1: return 0
    universe = make_n_triangular_grid_graph(n - 1)
    GraphSet.set_universe(universe)
    cycles = GraphSet.cycles()
    return cycles.len()
print([A266513(n) for n in range(1, 12)])  # Seiichi Manyama, Nov 30 2020