OFFSET
0,2
COMMENTS
Extended to a(0) using the formula/recurrence.
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Apr 07 2018
STATUS
approved