A350041 -id:A350041 - cp's OEIS frontend

A289893 Number of maximum independent vertex sets in the n-triangular honeycomb queen graph.

1, 3, 3, 2, 23, 18, 6, 270, 166, 28, 4842, 2532, 244, 120052, 49620, 2544, 3852972, 1270832, 35600, 156145080, 40668960, 659632, 7746956424, 1606984224, 15106128, 460265296128, 75930070688, 425802176

Offset: 1

Eric W. Weisstein, Jul 14 2017

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

Cf. A002047, A350041, A350191, A004396 (independence number).

a(3*n+1) agrees with A002047(n) for available terms.

a(18)-a(19) from Vaclav Kotesovec, Dec 13 2021
a(20) from Vaclav Kotesovec, Dec 16 2021
a(21)-a(28) from Martin Ehrenstein, Dec 17 2021

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.

cp's OEIS Frontend

A289893 Number of maximum independent vertex sets in the n-triangular honeycomb queen graph.

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