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A366508
a(n) = Lucas(2*n) + 2*(-1)^n + 1.
0
2, 10, 17, 50, 122, 325, 842, 2210, 5777, 15130, 39602, 103685, 271442, 710650, 1860497, 4870850, 12752042, 33385285, 87403802, 228826130, 599074577, 1568397610, 4106118242, 10749957125, 28143753122, 73681302250, 192900153617, 505019158610, 1322157322202
OFFSET
1,1
COMMENTS
For n >=3, number of independent vertex sets in the n-double cone graph.
LINKS
Eric Weisstein's World of Mathematics, Double Cone Graph
Eric Weisstein's World of Mathematics, Independent Vertex Set
FORMULA
a(n) = 3*a(n-1)-3*a(n-3)+a(n-4).
G.f.: x*(-2-4*x+13*x^2-5*x^3)/((x+1)*(x-1)*(x^2-3*x+1)).
MATHEMATICA
Table[LucasL[2 n] + 2 (-1)^n + 1, {n, 20}]
LinearRecurrence[{3, 0, -3, 1}, {2, 10, 17, 50}, 20]
CoefficientList[Series[(-2 - 4 x + 13 x^2 - 5 x^3)/(-1 + 3 x - 3 x^3 + x^4), {x, 0, 20}], x]
CROSSREFS
Cf. A005248 (bisection of the Lucas numbers).
Sequence in context: A214086 A127492 A258974 * A077247 A341032 A082939
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Oct 11 2023
STATUS
approved