A321247 Number of maximal independent vertex sets in the n X n fiveleaper graph.

1, 1, 1, 1, 16, 1540, 176460, 6332072, 81841692, 2434154301, 124866787929

Offset

1,5

Links

Table of n, a(n) for n=1..11.

Eric Weisstein's World of Mathematics, Fiveleaper Graph.

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

Mathematica

Table[Length@FindIndependentVertexSet[RelationGraph[EuclideanDistance[##] == 5 &, Tuples[Range[n], 2]], Infinity, All], {n, 8}]

Prog

(Python)
from networkx import empty_graph, find_cliques, complement
def A321247(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 ((5, 0), (-5, 0), (0, 5), (0, -5), (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 sum(1 for c in find_cliques(complement(G))) # Chai Wah Wu, Jan 11 2024

Crossrefs

Sequence in context: A266156 A054947 A071900 * A145406 A307924 A263387

Adjacent sequences: A321244 A321245 A321246 * A321248 A321249 A321250

Keyword

nonn,more

Author

Eric W. Weisstein, Nov 01 2018

Extensions

a(10) from Chai Wah Wu, Jan 17 2024

a(11) from Eric W. Weisstein, Jan 29 2024

Status

approved