A287393 -id:A287393 - cp's OEIS frontend

A099480 Count from 1, repeating 2*n 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

Paul Barry, Oct 18 2004

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

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-1).

Cf. A099479, A287393.

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

LinearRecurrence[{2, -2, 2, -2, 2, -1}, {1, 2, 2, 2, 2, 2}, 100] (* Vincenzo Librandi, Sep 09 2015 *)
Table[If[EvenQ[n],{n,n,n,n,n},n],{n,30}]//Flatten (* Harvey P. Dale, Dec 15 2020 *)

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

A287394 Domination number for camel's graph on a 2 X n board.

Original entry on oeis.org

0, 2, 4, 6, 6, 6, 6, 6, 6, 6, 8, 10, 12, 12, 12, 12, 12, 12, 12, 14, 16, 18, 18, 18, 18, 18, 18, 18, 20, 22, 24, 24, 24, 24, 24, 24, 24, 26, 28, 30, 30, 30, 30, 30, 30, 30, 32, 34, 36, 36, 36, 36, 36, 36, 36, 38, 40, 42, 42, 42, 42, 42, 42, 42, 44, 46, 48, 48

Offset: 0

David Nacin, May 24 2017

Minimum number of camels (from Tamerlane chess and fairy chess) required to dominate a 2 X n board.

			For n=4 we need a(4)=6 camels to dominate a 2 X 4 board.

Colin Barker, Table of n, a(n) for n = 0..1000
Wikipedia, Camel (chess)
Index entries for linear recurrences with constant coefficients, signature (2,-1,-1,2,-1,-1,2,-1).

Cf. A093390, A287393.

Table[2*(Floor[(i+6)/9]+Floor[(i+7)/9]+Floor[(i+8)/9]), {i, 0, 67}]

concat(0, Vec(2*x / ((1 - x)^2*(1 + x^3 + x^6)) + O(x^100))) \\ Colin Barker, May 27 2017

[2*(int((i+6)/9)+int((i+7)/9)+int((i+8)/9)) for i in range(68)]

a(n) = 2*(floor((n+6)/9) + floor((n+7)/9) + floor((n+8)/9)).
G.f.: 2*x / ((1 - x)^2*(1 + x^3 + x^6)). - Colin Barker, May 26 2017
a(n) = 2*A093390(n+6).

cp's OEIS Frontend

A099480 Count from 1, repeating 2*n five times.

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