OFFSET
1,1
COMMENTS
Extended to a(1)-a(3) using the formula/recurrence.
LINKS
Eric Weisstein's World of Mathematics, Total Dominating Set
Eric Weisstein's World of Mathematics, Wheel Graph
Index entries for linear recurrences with constant coefficients, signature (4, -5, 3, -2, -1, 2).
FORMULA
a(n) = A000032(n - 1) + 2*sin(n*Pi/2) + 2^(n - 1) - 1.
a(n) = 4*a(n-1) - 5*a(n-2) + 3*a(n-3) - 2*a(n-4) - a(n-5) + 2*a(n-6).
G.f.: x*(-4+14*x-16*x^2+7*x^3+3*x^5-2*x^4) / ( (x-1)*(2*x-1)*(x^2+x-1)*(x^2+1) ).
MATHEMATICA
Table[LucasL[n - 1] + 2 Sin[n Pi/2] + 2^(n - 1) - 1, {n, 20}]
LinearRecurrence[{4, -5, 3, -2, -1, 2}, {4, 2, 4, 11, 24, 42}, 20]
CoefficientList[Series[(-4 + 14 x - 16 x^2 + 7 x^3 - 2 x^4 + 3 x^5)/(-1 + 4 x - 5 x^2 + 3 x^3 - 2 x^4 - x^5 + 2 x^6), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Apr 10 2018
STATUS
approved