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URL: https://oeis.org/A287594

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A287594
Number of independent vertex sets in the n-helm graph.
0
3, 4, 12, 28, 72, 184, 480, 1264, 3360, 8992, 24192, 65344, 177024, 480640, 1307136, 3559168, 9699840, 26452480, 72173568, 196989952, 537802752, 1468536832, 4010582016, 10954043392, 29920862208, 81733033984, 223274237952, 609947435008, 1666309128192
OFFSET
0,1
COMMENTS
Extended to a(0)-a(2) using the formula.
LINKS
Eric Weisstein's World of Mathematics, Helm Graph
Eric Weisstein's World of Mathematics, Independent Vertex Set
FORMULA
a(n) = 2^n+A080040(n).
a(n) = 2^n+(1-sqrt(3))^n+(1+sqrt(3))^n.
a(n) = 4*a(n-1)-2*a(n-2)-4*a(n-3).
G.f.: (3-8*x+2*x^2)/((1-2*x)*(1-2*x-2*x^2)).
MATHEMATICA
Table[2^n + (1 - Sqrt[3])^n + (1 + Sqrt[3])^n, {n, 0, 20}] // Expand
Table[2^n + 2^(n/2) LucasL[n, Sqrt[2]], {n, 0, 20}] // Round
LinearRecurrence[{4, -2, -4}, {4, 12, 28}, {0, 20}]
CoefficientList[Series[(3 - 8 x + 2 x^2)/(1 - 4 x + 2 x^2 + 4 x^3), {x, 0, 20}], x]
CROSSREFS
Cf. A080040.
Sequence in context: A147569 A090660 A288140 * A296271 A000208 A079154
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, May 27 2017
STATUS
approved