A287394 -id:A287394 - cp's OEIS frontend

A093390 a(n) = floor(n/9) + floor((n+1)/9) + floor((n+2)/9).

0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 3, 3, 3, 3, 3, 3, 4, 5, 6, 6, 6, 6, 6, 6, 6, 7, 8, 9, 9, 9, 9, 9, 9, 9, 10, 11, 12, 12, 12, 12, 12, 12, 12, 13, 14, 15, 15, 15, 15, 15, 15, 15, 16, 17, 18, 18, 18, 18, 18, 18, 18, 19, 20, 21, 21, 21, 21, 21, 21, 21, 22, 23, 24, 24, 24, 24, 24, 24, 24, 25

Offset: 0

Reinhard Zumkeller, Mar 28 2004

Half the domination number of the camel's graph (from Tamerlane Chess) on a 2 X (n-6) chessboard. - David Nacin, May 28 2017

Michael De Vlieger, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (2,-1,-1,2,-1,-1,2,-1)

Cf. A004524, A093391, A093392, A093393, A287394.

Array[Total@ Map[Floor[#/9] &, # + Range[0, 2]] &, 80, 0] (* or *)
CoefficientList[Series[x^7/((x^6 + x^3 + 1) (x - 1)^2), {x, 0, 79}], x] (* Michael De Vlieger, Dec 12 2017 *)

a(n)=n\9+(n+1)\9+(n+2)\9 \\ Charles R Greathouse IV, Oct 16 2015

G.f.: x^7 / ( (x^6+x^3+1)*(x-1)^2 ). - R. J. Mathar, Mar 22 2011
a(n) = n/3 + O(1). - Charles R Greathouse IV, Oct 16 2015
a(n) = A287394(n-6)/2. - David Nacin, May 28 2017

A287393 Domination number for knight graph on a 2 X n board.

Original entry on oeis.org

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

Offset: 0

David Nacin, May 24 2017

Minimum number of knights required to dominate a 2 X n board.

			For n=3 we need a(3)=4 knights to dominate a 2 X 3 board.

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

Cf. A099480, A287394.

Table[2*(Floor[(i+4)/6]+Floor[(i+5)/6]), {i, 0, 67}]
LinearRecurrence[{2,-2,2,-2,2,-1},{0,2,4,4,4,4},70] (* Harvey P. Dale, Jul 07 2020 *)

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

[2*((i+4)//6+(i+5)//6) for i in range(68)]

a(n) = 2*(floor((n+4)/6) + floor((n+5)/6)).
From Colin Barker, May 26 2017: (Start)
G.f.: 2*x / ((1 - x)^2*(1 - x + x^2)*(1 + x + x^2)).
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) for n>5.
(End)
a(n) = 2*A099480(n-1).

cp's OEIS Frontend

A093390 a(n) = floor(n/9) + floor((n+1)/9) + floor((n+2)/9).

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