A286040 Matching number of the n X n antelope graph.

0, 0, 0, 0, 4, 12, 24, 28, 33, 40, 49, 60, 77, 98, 112, 124, 136, 156, 176, 200, 220, 242, 264, 288, 312, 338, 364, 392, 420, 450, 480, 512, 544, 578, 612, 648, 684, 722, 760, 800, 840, 882, 924, 968, 1012, 1058, 1104, 1152, 1200, 1250, 1300, 1352, 1404, 1458

Offset

1,5

Comments

It appears that a(n) = A007590(n) for n >= 20, which means that for these n, the antelope graph has a perfect matching if n is even and a matching with a single unmatched vertex if n is odd. - Pontus von Brömssen, May 01 2020

Links

Pontus von Brömssen, Table of n, a(n) for n = 1..128

Eric Weisstein's World of Mathematics, Antelope Graph.

Eric Weisstein's World of Mathematics, Matching.

Formula

Conjectures from Colin Barker, May 04 2020: (Start)

G.f.: x^5*(4 + 4*x - 12*x^3 - 3*x^4 + 10*x^5 + x^6 + 4*x^8 + 2*x^9 - 13*x^10 - 6*x^11 + 7*x^12 + 10*x^13 - 4*x^15 - 4*x^16 - 2*x^17 + 4*x^18) / ((1 - x)^3*(1 + x)).

a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n > 23.

(End)

Mathematica

Table[Length@FindIndependentEdgeSet[RelationGraph[Sort[Abs[Subtract[##]]] == {3, 4} &, Tuples[Range[n], 2]]], {n, 20}]
LinearRecurrence[{2, 0, -2, 1}, {0, 0, 0, 0, 4, 12, 24, 28, 33, 40, 49, 60, 77, 98, 112, 124, 136, 156, 176, 200, 220, 242, 264}, 60] (* Harvey P. Dale, Sep 05 2021 *)

Crossrefs

Cf. A007590.

Sequence in context: A319868 A274187 A353991 * A332608 A177464 A316985

Adjacent sequences: A286037 A286038 A286039 * A286041 A286042 A286043

Keyword

nonn

Author

Eric W. Weisstein, Jun 15 2017

Extensions

More terms from Pontus von Brömssen, May 01 2020

Status

approved