A288795 a(n) = 4^n + 3^(n + 1) - 2.

11, 41, 143, 497, 1751, 6281, 22943, 85217, 321191, 1225721, 4725743, 18371537, 71891831, 282784361, 1116788543, 4424107457, 17567289671, 69881738201, 278364691343, 1109971980977, 4429427570711, 17686329223241, 70651173714143, 282322265320097, 1128441772670951

Offset

1,1

Comments

Number of dominating sets in the n-book graph.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Book Graph

Eric Weisstein's World of Mathematics, Dominating Set

Index entries for linear recurrences with constant coefficients, signature (8,-19,12).

Formula

a(n) = 4^n + 3^(n + 1) - 2.

a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3).

G.f.: -((x*(11 - 47*x + 24*x^2))/((-1 + x)*(-1 + 3*x)*(-1 + 4*x))).

Mathematica

Table[4^n + 3^(n + 1) - 2, {n, 20}]
LinearRecurrence[{8, -19, 12}, {11, 41, 143}, 20]
CoefficientList[Series[-((11 - 47 x + 24 x^2)/((-1 + x) (-1 + 3 x) (-1 + 4 x))), {x, 0, 20}], x]

Prog

(Magma) [4^n+3^(n+1)-2: n in [1..30]]; // Vincenzo Librandi, Jun 30 2017

Crossrefs

Sequence in context: A268930 A139933 A243892 * A213659 A199209 A156733

Adjacent sequences: A288792 A288793 A288794 * A288796 A288797 A288798

Keyword

nonn,easy

Author

Eric W. Weisstein, Jun 29 2017

Status

approved