cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A360685 Number of maximum independent vertex sets in the n-halved cube graph Q_n/2.

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%I A360685 #14 Feb 16 2025 08:34:04
%S A360685 1,2,4,4,40,120,240,240,11612160
%N A360685 Number of maximum independent vertex sets in the n-halved cube graph Q_n/2.
%H A360685 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HalvedCubeGraph.html">Halved Cube Graph</a>.
%H A360685 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximumIndependentVertexSet.html">Maximum Independent Vertex Set</a>.
%t A360685 Table[With[{g = GraphPower[HypercubeGraph[n - 1], 2]}, Length[FindIndependentVertexSet[g, Length /@ FindIndependentVertexSet[g], All]]], {n, 8}]
%o A360685 (Python)
%o A360685 from collections import Counter
%o A360685 from networkx import empty_graph, find_cliques, complement, power
%o A360685 def A360685(n):
%o A360685     k = 1<<n-1
%o A360685     G = empty_graph(range(k))
%o A360685     G.add_edges_from((a,b) for a in range(k) for b in range(a) if (lambda m: not(m&-m)^m if m else False)(a^b))
%o A360685     return (c:=Counter(len(c) for c in find_cliques(complement(power(G,2)))))[max(c)] # _Chai Wah Wu_, Jan 12 2024
%Y A360685 Cf. A290606.
%K A360685 nonn,more,hard
%O A360685 1,2
%A A360685 _Eric W. Weisstein_, Feb 16 2023