A289893 -id:A289893 - cp's OEIS frontend

A289709 Number of independent vertex sets and vertex covers in the n-triangular honeycomb queen graph.

2, 4, 10, 28, 84, 272, 946, 3486, 13560, 55432, 236852, 1054928, 4881972, 23420436, 116204016, 595246848, 3142169416, 17068245184, 95267426432, 545732236936, 3204607199704

Offset: 1

Eric W. Weisstein, Jul 14 2017

Eric Weisstein's World of Mathematics, Independent Vertex Set
Eric Weisstein's World of Mathematics, Vertex Cover

Cf. A193986, A283117, A289883, A289893, A326611.

From Andrew Howroyd, Sep 12 2019: (Start)
a(n) = 6*A283117(n) - 2*A326611(n) - 3*2^ceiling(n/2).
a(n) = 1 + Sum_{k>=1} A193986(n,k).
(End)

a(13)-a(21) from Andrew Howroyd, Sep 12 2019

A350191 Number of ways of placing maximum number of nonattacking rooks on a triangular board with edge-length n (not counting rotations and reflections as distinct).

Original entry on oeis.org

1, 1, 1, 1, 5, 3, 1, 45, 29, 5, 807, 422, 29, 20022, 8270, 224, 642162, 211848, 3012

Offset: 1

Vaclav Kotesovec, Dec 19 2021

a(n) = A350041(n) for n <> 10,13,16,19,...

Conjecture: a(3*n-2) = A309260(n). There is a nice analogy with A289893(3*n+1) = A002047(n).

Alain Brobecker, Non Attacking Rooks on Hexhex and Triangular boards
Vaclav Kotesovec, Example: All non-identical positions for n = 10, a(10) = 5

Cf. A350041, A289893.

A350041 Number of ways of placing maximum number of nonattacking rooks on a triangular board with edge-length n (symmetric solutions count only once).

Original entry on oeis.org

1, 1, 1, 1, 5, 3, 1, 45, 29, 6, 807, 422, 46, 20022, 8270, 424, 642162, 211848

Offset: 1

Alain Brobecker, Dec 10 2021

The rooks placements are considered different when they cannot be obtained by a rotation and/or reflection of another solution that leaves the board inchanged. - Alain Brobecker, Dec 19 2021

a(n) = A350191(n) for n <> 10,13,16,19,... - Vaclav Kotesovec, Dec 20 2021

Alain Brobecker, Non Attacking Rooks on Hexhex and Triangular boards

Cf. A004396, A289893, A350191.

a(17)-a(18) from Vaclav Kotesovec, Dec 19 2021

A289883 Number of maximal independent vertex sets in the n-triangular honeycomb queen graph.

Original entry on oeis.org

1, 3, 3, 11, 23, 73, 211, 651, 2371, 7401, 30151, 107713, 456409, 1888753, 8148451, 37754791, 170459451, 842310755, 4096595827, 20984546901

Offset: 1

Eric W. Weisstein, Jul 14 2017

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

Cf. A289709, A289893.

a(14)-a(20) from Andrew Howroyd, Dec 03 2021

cp's OEIS Frontend

A289709 Number of independent vertex sets and vertex covers in the n-triangular honeycomb queen graph.

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A350191 Number of ways of placing maximum number of nonattacking rooks on a triangular board with edge-length n (not counting rotations and reflections as distinct).

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A350041 Number of ways of placing maximum number of nonattacking rooks on a triangular board with edge-length n (symmetric solutions count only once).

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Author

Keywords

Comments

Links

Crossrefs

Extensions

A289883 Number of maximal independent vertex sets in the n-triangular honeycomb queen graph.

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Author

Keywords

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