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.

Showing 1-4 of 4 results.

A333077 Number of maximal independent sets in the binary de Bruijn graph of order n.

Original entry on oeis.org

1, 2, 3, 8, 64, 2626, 4850838
Offset: 0

Views

Author

Pontus von Brömssen, Mar 07 2020

Keywords

Crossrefs

Programs

  • Python
    import networkx as nx
    def deBruijn(n):
        return nx.MultiDiGraph(((0, 0), (0, 0))) if n==0 else nx.line_graph(deBruijn(n-1))
    def A333077(n):
        return sum(1 for _ in nx.find_cliques(nx.complement(nx.Graph(deBruijn(n)))))
    # replacement of a function removed from NetworkX by Ross Barnowski, Nov 12 2023

A333078 Number of maximum independent sets in the binary de Bruijn graph of order n.

Original entry on oeis.org

1, 2, 1, 6, 2, 44, 8
Offset: 0

Views

Author

Pontus von Brömssen, Mar 07 2020

Keywords

Crossrefs

A359994 Independence number of the 2-Fibonacci digraph of order n.

Original entry on oeis.org

1, 1, 2, 3, 6, 9, 16, 25, 44, 67, 115
Offset: 1

Views

Author

Pontus von Brömssen, Jan 21 2023

Keywords

Comments

See Dalfó and Fiol (2019) or A360000 for the definition of the 2-Fibonacci graph.
a(12) >= 179. - Pontus von Brömssen, Nov 12 2023

Crossrefs

Programs

  • Python
    import networkx as nx
    def F(n): return nx.DiGraph(((0,0),(0,1),(1,0))) if n == 1 else nx.line_graph(F(n-1))
    def A359994(n): return nx.max_weight_clique(nx.complement(nx.Graph(F(n))),weight=None)[1]

A258935 Independence number of Keller graphs.

Original entry on oeis.org

4, 5, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592
Offset: 1

Views

Author

Stan Wagon, Nov 06 2015

Keywords

Examples

			For G(2), a maximum independent set is {03,10,12,13,23}.
		

References

  • W. Jarnicki, W. Myrvold, P. Saltzman, S. Wagon, Properties, proved and conjectured, of Keller, queen, and Mycielski graphs, Ars Mathematica Contemporanea 13:2 (2017) 427-460.

Crossrefs

Essentially the same as A143858, A240951, A198633, A171497, A151821, A146541 and A077552.

Programs

Formula

a(n) = 2^n except a(1) = 4 and a(2) = 5.
G.f.: x*(x*(3+2*x)-4)/(2*x-1), e.g.f.: exp(2*x)+x^2/2+2*x-1. - Benedict W. J. Irwin, Jul 15 2016
Showing 1-4 of 4 results.