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A286069
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Independence and clique covering number of the n X n antelope graph.
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1
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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
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refs;
listen;
history;
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internal format)
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OFFSET
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1,2
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LINKS
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FORMULA
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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
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MATHEMATICA
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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}]]
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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