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
KEYWORD
nonn,easy
AUTHOR
David Nacin, May 24 2017
STATUS
approved