A099480 Count from 1, repeating 2n five times.

1, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 7, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 13, 14, 14, 14, 14, 14, 15, 16, 16, 16, 16, 16, 17, 18, 18, 18, 18, 18, 19, 20, 20, 20, 20, 20, 21, 22, 22, 22, 22, 22, 23, 24, 24, 24, 24, 24, 25, 26, 26, 26, 26, 26

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

Table of n, a(n) for n=0..77.

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

Cf. A099479, A287393.

Sequence in context: A197054 A337926 A120502 * A025783 A025780 A199121

Adjacent sequences: A099477 A099478 A099479 * A099481 A099482 A099483

Keyword

easy,nonn

Author

Paul Barry, Oct 18 2004

Status

approved