OFFSET
0,1
COMMENTS
Extended to a(0)-a(2) using the formula.
LINKS
Eric Weisstein's World of Mathematics, Helm Graph
Eric Weisstein's World of Mathematics, Independent Vertex Set
Index entries for linear recurrences with constant coefficients, signature (4, -2, -4).
FORMULA
a(n) = 2^n+A080040(n).
a(n) = 2^n+(1-sqrt(3))^n+(1+sqrt(3))^n.
a(n) = 4*a(n-1)-2*a(n-2)-4*a(n-3).
G.f.: (3-8*x+2*x^2)/((1-2*x)*(1-2*x-2*x^2)).
MATHEMATICA
Table[2^n + (1 - Sqrt[3])^n + (1 + Sqrt[3])^n, {n, 0, 20}] // Expand
Table[2^n + 2^(n/2) LucasL[n, Sqrt[2]], {n, 0, 20}] // Round
LinearRecurrence[{4, -2, -4}, {4, 12, 28}, {0, 20}]
CoefficientList[Series[(3 - 8 x + 2 x^2)/(1 - 4 x + 2 x^2 + 4 x^3), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, May 27 2017
STATUS
approved