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
KEYWORD
nonn,changed
AUTHOR
Eric W. Weisstein, Jun 15 2017
EXTENSIONS
More terms from Pontus von Brömssen, May 01 2020
STATUS
approved