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A302402 Total domination number of the n-ladder graph. 2
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 (list; graph; refs; listen; history; text; internal format)
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)).

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: A187324 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

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Last modified May 20 12:33 EDT 2019. Contains 323422 sequences. (Running on oeis4.)