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

%I A287394 #27 Nov 23 2024 03:34:38
%S A287394 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,
%T A287394 18,18,20,22,24,24,24,24,24,24,24,26,28,30,30,30,30,30,30,30,32,34,36,
%U A287394 36,36,36,36,36,36,38,40,42,42,42,42,42,42,42,44,46,48,48
%N A287394 Domination number for camel's graph on a 2 X n board.
%C A287394 Minimum number of camels (from Tamerlane chess and fairy chess) required to dominate a 2 X n board.
%H A287394 Colin Barker, <a href="/A287394/b287394.txt">Table of n, a(n) for n = 0..1000</a>
%H A287394 Wikipedia, <a href="https://en.wikipedia.org/wiki/Camel_(chess)">Camel (chess)</a>
%H A287394 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,-1,2,-1,-1,2,-1).
%F A287394 a(n) = 2*(floor((n+6)/9) + floor((n+7)/9) + floor((n+8)/9)).
%F A287394 G.f.: 2*x / ((1 - x)^2*(1 + x^3 + x^6)). - _Colin Barker_, May 26 2017
%F A287394 a(n) = 2*A093390(n+6).
%e A287394 For n=4 we need a(4)=6 camels to dominate a 2 X 4 board.
%t A287394 Table[2*(Floor[(i+6)/9]+Floor[(i+7)/9]+Floor[(i+8)/9]), {i, 0, 67}]
%o A287394 (Python) [2*(int((i+6)/9)+int((i+7)/9)+int((i+8)/9)) for i in range(68)]
%o A287394 (PARI) concat(0, Vec(2*x / ((1 - x)^2*(1 + x^3 + x^6)) + O(x^100))) \\ _Colin Barker_, May 27 2017
%Y A287394 Cf. A093390, A287393.
%K A287394 nonn,easy
%O A287394 0,2
%A A287394 _David Nacin_, May 24 2017