OFFSET
1,2
COMMENTS
Extended to a(1)-a(2) 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 (4, -6, 4, 0, -2, 1).
FORMULA
a(n) = n - 2*cos(n*Pi/3) + Lucas(n).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - 2*a(n-5) + a(n-6).
G.f.: x*(-1 - 2*x + 9*x^2 - 8*x^3 + 3*x^4)/((-1+x)^2 *(x^2+x-1) *(x^2-x+1)).
MATHEMATICA
Table[n - 2 Cos[n Pi/3] + LucasL[n], {n, 20}]
LinearRecurrence[{4, -6, 4, 0, -2, 1}, {1, 6, 9, 12, 15, 22}, 20]
CoefficientList[Series[(-1 - 2 x + 9 x^2 - 8 x^3 + 3 x^4)/((-1 + x)^2 (-1 + 2 x - x^2 + x^4)), {x, 0, 20}], x]
PROG
(PARI) x='x+O('x^23); Vec((-1 - 2*x + 9*x^2 - 8*x^3 + 3*x^4)/((-1 + x)^2* (-1 + 2*x - x^2 + x^4))) \\ Georg Fischer, Apr 03 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jan 02 2018
EXTENSIONS
Terms a(1), a(2) prepended by Georg Fischer, Apr 03 2019
STATUS
approved