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%I #29 Jan 27 2024 18:51:44
%S 1,4,9,16,21,24,25,36,48,60,72,84,92,98,113,132,153,168,185,200,221,
%T 242,265,288,313,338,365,392,421,450,481,512,545,578,613,648,685,722,
%U 761,800,841,882,925,968,1013,1058,1105,1152,1201,1250,1301,1352,1405,1458,1513
%N Independence and clique covering number of the n X n antelope graph.
%H Colin Barker, <a href="/A286069/b286069.txt">Table of n, a(n) for n = 1..1000</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/CliqueCoveringNumber.html">Clique Covering Number</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IndependenceNumber.html">Independence Number</a>.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F a(n) = 2*(a-1) - 2*a(n-3) + a(n-4) for n >= 24. - _Eric W. Weisstein_, Apr 19 2019
%F G.f.: x*(1 + 2*x + x^2 - 4*x^4 - 4*x^5 + 12*x^7 + 3*x^8 - 10*x^9 - x^10 - 4*x^12 - 2*x^13 + 13*x^14 + 6*x^15 - 7*x^16 - 10*x^17 + 4*x^19 + 4*x^20 + 2*x^21 - 4*x^22) / ((1 - x)^3*(1 + x)). - _Colin Barker_, Apr 19 2019
%t Table[Length@First@FindIndependentVertexSet[RelationGraph[Sort[Abs[Subtract[##]]] == {3, 4} &, Tuples[Range[n], 2]]], {n, 13}]
%t Join[{1, 4, 9, 16, 21, 24, 25, 36, 48, 60, 72, 84, 92, 98, 113, 132, 153, 168, 185}, LinearRecurrence[{2, 0, -2, 1}, {1, 2, 5, 8}, {20, 40}]]
%o (PARI) Vec(x*(1 + 2*x + x^2 - 4*x^4 - 4*x^5 + 12*x^7 + 3*x^8 - 10*x^9 - x^10 - 4*x^12 - 2*x^13 + 13*x^14 + 6*x^15 - 7*x^16 - 10*x^17 + 4*x^19 + 4*x^20 + 2*x^21 - 4*x^22) / ((1 - x)^3*(1 + x)) + O(x^60)) \\ _Colin Barker_, Apr 19 2019
%K nonn,easy
%O 1,2
%A _Eric W. Weisstein_, Jun 15 2017
%E Extended by _Eric W. Weisstein_, Apr 18 2019
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