A286040 - OEIS

%I #33 Jan 27 2024 18:51:59

%S 0,0,0,0,4,12,24,28,33,40,49,60,77,98,112,124,136,156,176,200,220,242,

%T 264,288,312,338,364,392,420,450,480,512,544,578,612,648,684,722,760,

%U 800,840,882,924,968,1012,1058,1104,1152,1200,1250,1300,1352,1404,1458

%N Matching number of the n X n antelope graph.

%C 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

%H Pontus von Brömssen, <a href="/A286040/b286040.txt">Table of n, a(n) for n = 1..128</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AntelopeGraph.html">Antelope Graph</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Matching.html">Matching</a>.

%F Conjectures from _Colin Barker_, May 04 2020: (Start)

%F 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)).

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

%F (End)

%t Table[Length@FindIndependentEdgeSet[RelationGraph[Sort[Abs[Subtract[##]]] == {3, 4} &, Tuples[Range[n], 2]]], {n, 20}]

%t 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 *)

%Y Cf. A007590.

%K nonn

%O 1,5

%A _Eric W. Weisstein_, Jun 15 2017

%E More terms from _Pontus von Brömssen_, May 01 2020