OFFSET
1,1
COMMENTS
Sequence extended to a(1) using the formula/recurrence.
LINKS
Eric Weisstein's World of Mathematics, Minimum Dominating Set
Eric Weisstein's World of Mathematics, Pan Graph
Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1).
FORMULA
a(n) = 1 for n = 0 (mod 3)
(n^2+7*n+28)/18 for n = 1 (mod 3)
(n+1)/3 for n = 2 (mod 3).
a(n) = 3*a(n-3)-3*a(n-6)+a(n-9) for n>9.
G.f.: -x*(2 + x + x^2 - 2*x^3 - x^4 - 2*x^5 + x^6 + x^8)/((-1 + x)^3*(1 + x + x^2)^3).
MATHEMATICA
Table[Piecewise[{{1, Mod[n, 3] == 0}, {(28 + 7 n + n^2)/18, Mod[n, 3] == 1}, {(n + 1)/3, Mod[n, 3] == 2}}], {n, 20}]
LinearRecurrence[{0, 0, 3, 0, 0, -3, 0, 0, 1}, {2, 1, 1, 4, 2, 1, 7, 3, 1}, 20]
CoefficientList[Series[-(2 + x + x^2 - 2 x^3 - x^4 - 2 x^5 + x^6 + x^8)/((-1 + x)^3 (1 + x + x^2)^3), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Sep 09 2021
STATUS
approved