OFFSET
0,2
COMMENTS
Sequence extended to a(0)-a(1) using the formula/recurrence.
LINKS
Eric Weisstein's World of Mathematics, Chordless Cycle
Eric Weisstein's World of Mathematics, Moebius Ladder
Index entries for linear recurrences with constant coefficients, signature (2,1,2,-1).
FORMULA
a(n) = A005248(n) - 2*cos(2*n*Pi/3).
a(n) = 2*a(n-1) + a(n-2) + 2*a(n-3) - a(n-4).
G.f.: -4*x*(x-1)*(1+x) / ( (x^2-3*x+1)*(1+x+x^2) ).
E.g.f.: 2*exp(-x/2)*(exp(2*x)*cosh(sqrt(5)*x/2) - cos(sqrt(3)*x/2)). - Stefano Spezia, Jul 21 2022
MATHEMATICA
Table[LucasL[2 n] - 2 Cos[2 n Pi/3], {n, 0, 20}]
LinearRecurrence[{2, 1, 2, -1}, {0, 4, 8, 16}, 20]
CoefficientList[Series[-4 x (-1 + x^2)/(1 - 2 x - x^2 - 2 x^3 + x^4), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Mar 26 2018
STATUS
approved