A368189 Number of (undirected) cycles in the n-Pell graph.

0, 1, 65, 4983940

Offset

1,3

Links

Table of n, a(n) for n=1..4.

Eric Weisstein's World of Mathematics, Graph Cycle.

Eric Weisstein's World of Mathematics, Pell Graph.

Prog

(Python)
from itertools import product, combinations, groupby, islice
from networkx import empty_graph, simple_cycles
def A368189(n):
    if n<=1 : return 0
    G = empty_graph(v for v in product((0, 1, 2), repeat=n) if not any(len(list(g))&1 and k==2 for k, g in groupby(v)))
    for a, b in combinations(G, 2):
        r = tuple(islice((i for i in range(n) if a[i]!=b[i]), 3))
        if len(r)==1 and a[r[0]]!=2 and b[r[0]]!=2:
                G.add_edge(a, b)
        elif len(r)==2 and r[0]+1==r[1] and a[r[0]] and b[r[0]] and a[r[0]]==a[r[1]] and b[r[0]]==b[r[1]]:
                G.add_edge(a, b)
    return sum(1 for c in simple_cycles(G)) # Chai Wah Wu, Jan 18 2024

Crossrefs

Sequence in context: A238612 A185823 A035519 * A238842 A059755 A215657

Adjacent sequences: A368186 A368187 A368188 * A368190 A368191 A368192

Keyword

nonn,more

Author

Eric W. Weisstein, Dec 16 2023

Status

approved