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A286069
Independence and clique covering number of the n X n antelope graph.
1
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
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.
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 15 2017
EXTENSIONS
Extended by Eric W. Weisstein, Apr 18 2019
STATUS
approved