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

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

0,2

Comments

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

Links

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).

Formula

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).

Example

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

Mathematica

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

Prog

(Python) [2*(int((i+6)/9)+int((i+7)/9)+int((i+8)/9)) for i in range(68)]
(PARI) concat(0, Vec(2*x / ((1 - x)^2*(1 + x^3 + x^6)) + O(x^100))) \\ Colin Barker, May 27 2017

Crossrefs

Cf. A093390, A287393.

Sequence in context: A054584 A049041 A092337 * A302754 A225369 A296511

Adjacent sequences: A287391 A287392 A287393 * A287395 A287396 A287397

Keyword

nonn,easy

Author

David Nacin, May 24 2017

Status

approved