A286069 Independence and clique covering number of the n X n antelope graph.

1, 4, 9, 16, 21, 24, 25, 36, 48, 60, 72, 84, 92, 98, 113, 132, 153, 168, 185, 200, 221, 242, 265, 288, 313, 338, 365, 392, 421, 450, 481, 512, 545, 578, 613, 648, 685, 722, 761, 800, 841, 882, 925, 968, 1013, 1058, 1105, 1152, 1201, 1250, 1301, 1352, 1405, 1458, 1513

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Antelope Graph.

Eric Weisstein's World of Mathematics, Clique Covering Number.

Eric Weisstein's World of Mathematics, Independence Number.

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Formula

a(n) = 2*(a-1) - 2*a(n-3) + a(n-4) for n >= 24. - Eric W. Weisstein, Apr 19 2019

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

Mathematica

Table[Length@First@FindIndependentVertexSet[RelationGraph[Sort[Abs[Subtract[##]]] == {3, 4} &, Tuples[Range[n], 2]]], {n, 13}]
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}]]

Prog

(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

Crossrefs

Sequence in context: A313340 A010461 A010421 * A010445 A155570 A313341

Adjacent sequences: A286066 A286067 A286068 * A286070 A286071 A286072

Keyword

nonn,easy

Author

Eric W. Weisstein, Jun 15 2017

Extensions

Extended by Eric W. Weisstein, Apr 18 2019

Status

approved