OFFSET
0,2
COMMENTS
Could be called the Jones sequence of the knot 9_43, since the g.f. is the reciprocal of (a parameterization of) the Jones polynomial for 9_43.
Half the domination number of the knight's graph on a 2 X (n+1) chessboard. - David Nacin, May 28 2017
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-1).
FORMULA
G.f.: 1/((1-x+x^2)(1-x-x^3+x^4)) = 1/(1-2x+2x^2-2x^3+2x^4-2x^5+x^6);
a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-2*a(n-4)+2*a(n-5)-a(n-6), n>5;
a(n) = -cos(Pi*2n/3+Pi/3)/6+sqrt(3)*sin(Pi*2n/3+Pi/3)/18-sqrt(3)*cos(Pi*n/3+Pi/6)/6+sin(Pi*n/3+Pi/6)/2+(n+3)/3.
a(n) = Sum_{i=0..n+1} floor((i-1)/6) - floor((i-3)/6). - Wesley Ivan Hurt, Sep 08 2015
a(n) = A287393(n+1)/2. - David Nacin, May 28 2017
MATHEMATICA
LinearRecurrence[{2, -2, 2, -2, 2, -1}, {1, 2, 2, 2, 2, 2}, 100] (* Vincenzo Librandi, Sep 09 2'15 *)
Table[If[EvenQ[n], {n, n, n, n, n}, n], {n, 30}]//Flatten (* Harvey P. Dale, Dec 15 2020 *)
PROG
(Magma) I:=[1, 2, 2, 2, 2, 2]; [n le 6 select I[n] else 2*Self(n-1)-2*Self(n-2)+2*Self(n-3)-2*Self(n-4)+2*Self(n-5)-Self(n-6): n in [1..100]]; // Vincenzo Librandi, Sep 09 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 18 2004
STATUS
approved