OFFSET
1,1
COMMENTS
Sequence extended to a(1) using the formula/recurrence.
LINKS
Eric Weisstein's World of Mathematics, Dipyramidal Graph
Eric Weisstein's World of Mathematics, Total Dominating Set
Index entries for linear recurrences with constant coefficients, signature (4,-5,3,-2,-1,2).
FORMULA
a(n) = Lucas(n) + 2*cos(n*Pi/2) + 3*2^n - 3.
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 - 6*x + 5*x^2 - 8*x^3 - 9*x^4 + 8*x^5)/((-1 + x)*(-1 +
2*x)*(1 + x^2)*(-1 + x + x^2)).
MATHEMATICA
Table[LucasL[n] + 2 Cos[n Pi/2] + 3 2^n - 3, {n, 50}]
LinearRecurrence[{4, -5, 3, -2, -1, 2}, {4, 10, 25, 54, 104, 205}, 20]
CoefficientList[Series[-(4 - 6 x + 5 x^2 - 8 x^3 - 9 x^4 + 8 x^5)/((-1 + x) (-1 + 2 x) (1 + x^2) (-1 + x + x^2)), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Sep 03 2021
STATUS
approved