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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 15 2017
EXTENSIONS
Extended by Eric W. Weisstein, Apr 18 2019
STATUS
approved