A290718 a(n) = 2^(n + 1) + 4^(n - 1) - 2.

3, 10, 30, 94, 318, 1150, 4350, 16894, 66558, 264190, 1052670, 4202494, 16793598, 67141630, 268500990, 1073872894, 4295229438, 17180393470, 68720525310, 274880004094, 1099515822078, 4398054899710, 17592202821630, 70368777732094, 281475043819518, 1125900041060350, 4503599895805950, 18014399046352894, 72057595111669758

Offset

1,1

Comments

For n > 2, also the number of connected (non-null) induced subgraphs in the n-barbell graph.

Links

Table of n, a(n) for n=1..29.

Eric Weisstein's World of Mathematics, Barbell Graph

Eric Weisstein's World of Mathematics, Connected Graph

Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph

Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Formula

a(n) = 2^(n + 1) + 4^(n - 1) - 2.

a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3).

G.f.: (x (-3 + 11 x - 2 x^2))/(-1 + 7 x - 14 x^2 + 8 x^3).

Mathematica

Table[2^(n + 1) + 4^(n - 1) - 2, {n, 20}]
LinearRecurrence[{7, -14, 8}, {3, 10, 30}, 40]
CoefficientList[Series[(-3 + 11 x - 2 x^2)/(-1 + 7 x - 14 x^2 + 8 x^3), {x, 0, 20}], x]

Prog

(PARI) a(n)=2^(n+1)+4^(n-1)-2 \\ Charles R Greathouse IV, Aug 09 2017

Crossrefs

Sequence in context: A269800 A033113 A360714 * A300421 A302289 A003441

Adjacent sequences: A290715 A290716 A290717 * A290719 A290720 A290721

Keyword

nonn,easy

Author

Eric W. Weisstein, Aug 09 2017

Status

approved