A302402 Total domination number of the n-ladder graph.

0, 2, 2, 2, 4, 4, 4, 6, 6, 6, 8, 8, 8, 10, 10, 10, 12, 12, 12, 14, 14, 14, 16, 16, 16, 18, 18, 18, 20, 20, 20, 22, 22, 22, 24, 24, 24, 26, 26, 26, 28, 28, 28, 30, 30, 30, 32, 32, 32, 34, 34, 34, 36, 36, 36, 38, 38, 38, 40, 40, 40, 42, 42, 42, 44, 44, 44, 46, 46, 46, 48

Offset

0,2

Comments

Extended to a(0) using the formula/recurrence.

Links

Table of n, a(n) for n=0..70.

Eric Weisstein's World of Mathematics, Ladder Graph

Eric Weisstein's World of Mathematics, Total Domination Number

Index entries for linear recurrences with constant coefficients, signature (1, 0, 1, -1).

Formula

a(n) = 2*floor((n + 2)/3).

a(n) = 2/9*(3 + 3*n - 3*cos(2*n*Pi/3) + sqrt(3)*sin(2*n*Pi/3)).

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

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

a(n) = 2*A002264(n+2). - R. J. Mathar, May 02 2023

Mathematica

Table[2 Floor[(n + 2)/3], {n, 0, 20}]
2 Floor[(Range[0, 20] + 2)/3]
Table[2/9 (3 + 3 n - 3 Cos[2 n Pi/3] + Sqrt[3] Sin[2 n Pi/3]), {n, 0, 20}]
LinearRecurrence[{1, 0, 1, -1}, {2, 2, 2, 4}, {0, 20}]
CoefficientList[Series[2 x/((-1 + x)^2 (1 + x + x^2)), {x, 0, 20}], x]

Crossrefs

Sequence in context: A334207 A323094 A086227 * A079438 A123050 A113694

Adjacent sequences: A302399 A302400 A302401 * A302403 A302404 A302405

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 07 2018

Status

approved