A389172 a(n) = 2^(n+1) + 4^(n-1) - 1.

4, 11, 31, 95, 319, 1151, 4351, 16895, 66559, 264191, 1052671, 4202495, 16793599, 67141631, 268500991, 1073872895, 4295229439, 17180393471, 68720525311, 274880004095, 1099515822079, 4398054899711, 17592202821631, 70368777732095, 281475043819519

Offset

1,1

Comments

For n >= 3, also the number of mutual-visibility sets in the n-barbell graph.

Links

Matthew L. LaSelle, Table of n, a(n) for n = 1..500

Eric Weisstein's World of Mathematics, Barbell Graph.

Eric Weisstein's World of Mathematics, Visibility Polynomial.

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

Formula

G.f.: -x*(4-17*x+10*x^2)/((-1+x)*(-1+2*x)*(-1+4*x)).

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

From Hugo Pfoertner, Sep 26 2025: (Start)

a(n) = A290718(n) + 1.

a(n) = 64*A164051(n-4) - 1 for n>=5. (End)

Mathematica

Table[4^(n - 1) + 2^(n + 1) - 1, {n, 20}]
LinearRecurrence[{7, -14, 8}, {4, 11, 31}, 20]
CoefficientList[Series[-(4 - 17 x + 10 x^2)/((-1 + x) (-1 + 2 x) (-1 + 4 x)), {x, 0, 20}], x]

Crossrefs

Cf. A164051, A290718.

Sequence in context: A282856 A296572 A176573 * A134597 A076730 A084757

Adjacent sequences: A389169 A389170 A389171 * A389173 A389174 A389175

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 25 2025

Status

approved