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

%I A290607 #16 Feb 16 2025 08:33:50
%S A290607 1,56,1712,46336,1570048,76425216
%N A290607 Number of maximal independent vertex sets (and minimal vertex covers) in the n-Keller graph.
%H A290607 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KellerGraph.html">Keller Graph</a>
%H A290607 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximalIndependentVertexSet.html">Maximal Independent Vertex Set</a>
%H A290607 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalVertexCover.html">Minimal Vertex Cover</a>
%o A290607 (Python)
%o A290607 from itertools import zip_longest
%o A290607 from sympy.ntheory.factor_ import digits
%o A290607 from networkx import empty_graph, find_cliques
%o A290607 def A290607(n):
%o A290607     k = 1<<(n<<1)
%o A290607     G = empty_graph(range(k))
%o A290607     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)
%o A290607     return sum(1 for c in find_cliques(G)) # _Chai Wah Wu_, Jan 11 2024
%Y A290607 Cf. A258935, A284854.
%K A290607 nonn,more
%O A290607 1,2
%A A290607 _Eric W. Weisstein_, Aug 07 2017
%E A290607 a(5) from _Eric W. Weisstein_, Nov 05 2018
%E A290607 a(6) from _Chai Wah Wu_, Jan 11 2024