A290607 Number of maximal independent vertex sets (and minimal vertex covers) in the n-Keller graph.

1, 56, 1712, 46336, 1570048, 76425216

Offset

1,2

Links

Table of n, a(n) for n=1..6.

Eric Weisstein's World of Mathematics, Keller Graph

Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set

Eric Weisstein's World of Mathematics, Minimal Vertex Cover

Prog

(Python)
from itertools import zip_longest
from sympy.ntheory.factor_ import digits
from networkx import empty_graph, find_cliques
def A290607(n):
    k = 1<<(n<<1)
    G = empty_graph(range(k))
    G.add_edges_from((a, b) for a in range(k) for b in range(a) if (s:=tuple(c-d&3 for c, d in zip_longest(digits(a, 4)[-1:0:-1], digits(b, 4)[-1:0:-1], fillvalue=0))).count(2)==0 or s.count(0)>len(s)-2)
    return sum(1 for c in find_cliques(G)) # Chai Wah Wu, Jan 11 2024

Crossrefs

Cf. A258935, A284854.

Sequence in context: A278362 A017719 A234761 * A258465 A050989 A333067

Adjacent sequences: A290604 A290605 A290606 * A290608 A290609 A290610

Keyword

nonn,more

Author

Eric W. Weisstein, Aug 07 2017

Extensions

a(5) from Eric W. Weisstein, Nov 05 2018

a(6) from Chai Wah Wu, Jan 11 2024

Status

approved