A370198 Number of maximum independent vertex sets in the n X n antelope graph.

1, 1, 1, 1, 1, 1, 8, 4, 4, 4, 4, 4, 1, 2, 290

Offset

1,7

Links

Table of n, a(n) for n=1..15.

Eric Weisstein's World of Mathematics, Antelope Graph.

Eric Weisstein's World of Mathematics, Maximum Independent Vertex Set.

Mathematica

Table[Length@With[{g = RelationGraph[Sort[Abs[Subtract[##]]] == {3, 4} &, Tuples[Range[n], {2}]]}, FindIndependentVertexSet[g, Length /@ FindIndependentVertexSet[g], All]], {n, 8}]

Prog

(Python)
from collections import Counter
from networkx import empty_graph, find_cliques, complement
def A370198(n):
    G = empty_graph((i, j) for i in range(n) for j in range(n))
    G.add_edges_from(((i, j), (i+k, j+l)) for i in range(n) for j in range(n) for (k, l) in ((3, 4), (3, -4), (-3, 4), (-3, -4), (4, 3), (4, -3), (-4, 3), (-4, -3)) if 0<=i+k<n and 0<=j+l<n)
    return (x:=Counter(len(c) for c in find_cliques(complement(G))))[max(x)] # Chai Wah Wu, Feb 12 2024

Crossrefs

Sequence in context: A197033 A245720 A229495 * A131921 A129105 A226276

Adjacent sequences: A370195 A370196 A370197 * A370199 A370200 A370201

Keyword

nonn,more,hard

Author

Eric W. Weisstein, Feb 11 2024

Status

approved